3.4: Difference between revisions

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{{DISPLAYTITLE:Numerical Methods - 3.4 Differentiation}}
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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex1 3.4#Ex1] || [[Item:Q1187|<math>B_{-1}^{3} = -\tfrac{1}{6}(2-6t+3t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{3} = -\tfrac{1}{6}(2-6t+3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(3) = -(1)/(6)*(2 - 6*t + 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(3) == -Divide[1,6]*(2 - 6*t + 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex1 3.4#Ex1] || <math qid="Q1187">B_{-1}^{3} = -\tfrac{1}{6}(2-6t+3t^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{3} = -\tfrac{1}{6}(2-6t+3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(3) = -(1)/(6)*(2 - 6*t + 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(3) == -Divide[1,6]*(2 - 6*t + 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex2 3.4#Ex2] || [[Item:Q1188|<math>B_{0}^{3} = -\tfrac{1}{2}(1+4t-3t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{3} = -\tfrac{1}{2}(1+4t-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(3) = -(1)/(2)*(1 + 4*t - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(3) == -Divide[1,2]*(1 + 4*t - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex2 3.4#Ex2] || <math qid="Q1188">B_{0}^{3} = -\tfrac{1}{2}(1+4t-3t^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{3} = -\tfrac{1}{2}(1+4t-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(3) = -(1)/(2)*(1 + 4*t - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(3) == -Divide[1,2]*(1 + 4*t - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex3 3.4#Ex3] || [[Item:Q1189|<math>B_{1}^{3} = \tfrac{1}{2}(2+2t-3t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{3} = \tfrac{1}{2}(2+2t-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(3) = (1)/(2)*(2 + 2*t - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(3) == Divide[1,2]*(2 + 2*t - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex3 3.4#Ex3] || <math qid="Q1189">B_{1}^{3} = \tfrac{1}{2}(2+2t-3t^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{3} = \tfrac{1}{2}(2+2t-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(3) = (1)/(2)*(2 + 2*t - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(3) == Divide[1,2]*(2 + 2*t - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex4 3.4#Ex4] || [[Item:Q1190|<math>B_{2}^{3} = -\tfrac{1}{6}(1-3t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{3} = -\tfrac{1}{6}(1-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(3) = -(1)/(6)*(1 - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(3) == -Divide[1,6]*(1 - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex4 3.4#Ex4] || <math qid="Q1190">B_{2}^{3} = -\tfrac{1}{6}(1-3t^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{3} = -\tfrac{1}{6}(1-3t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(3) = -(1)/(6)*(1 - 3*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(3) == -Divide[1,6]*(1 - 3*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex5 3.4#Ex5] || [[Item:Q1192|<math>B_{-2}^{4} = \tfrac{1}{12}(1-t-3t^{2}+2t^{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{4} = \tfrac{1}{12}(1-t-3t^{2}+2t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(4) = (1)/(12)*(1 - t - 3*(t)^(2)+ 2*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(4) == Divide[1,12]*(1 - t - 3*(t)^(2)+ 2*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex5 3.4#Ex5] || <math qid="Q1192">B_{-2}^{4} = \tfrac{1}{12}(1-t-3t^{2}+2t^{3})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{4} = \tfrac{1}{12}(1-t-3t^{2}+2t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(4) = (1)/(12)*(1 - t - 3*(t)^(2)+ 2*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(4) == Divide[1,12]*(1 - t - 3*(t)^(2)+ 2*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex6 3.4#Ex6] || [[Item:Q1193|<math>B_{-1}^{4} = -\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{4} = -\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(4) = -(1)/(6)*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(4) == -Divide[1,6]*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex6 3.4#Ex6] || <math qid="Q1193">B_{-1}^{4} = -\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{4} = -\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(4) = -(1)/(6)*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(4) == -Divide[1,6]*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex7 3.4#Ex7] || [[Item:Q1194|<math>B_{0}^{4} = -\tfrac{1}{2}t(5-2t^{2})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{4} = -\tfrac{1}{2}t(5-2t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(4) = -(1)/(2)*t*(5 - 2*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(4) == -Divide[1,2]*t*(5 - 2*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex7 3.4#Ex7] || <math qid="Q1194">B_{0}^{4} = -\tfrac{1}{2}t(5-2t^{2})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{4} = -\tfrac{1}{2}t(5-2t^{2})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(4) = -(1)/(2)*t*(5 - 2*(t)^(2))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(4) == -Divide[1,2]*t*(5 - 2*(t)^(2))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex8 3.4#Ex8] || [[Item:Q1195|<math>B_{1}^{4} = \tfrac{1}{6}(4+8t-3t^{2}-4t^{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{4} = \tfrac{1}{6}(4+8t-3t^{2}-4t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(4) = (1)/(6)*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(4) == Divide[1,6]*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex8 3.4#Ex8] || <math qid="Q1195">B_{1}^{4} = \tfrac{1}{6}(4+8t-3t^{2}-4t^{3})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{4} = \tfrac{1}{6}(4+8t-3t^{2}-4t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(4) = (1)/(6)*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(4) == Divide[1,6]*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex9 3.4#Ex9] || [[Item:Q1196|<math>B_{2}^{4} = -\tfrac{1}{12}(1+t-3t^{2}-2t^{3})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{4} = -\tfrac{1}{12}(1+t-3t^{2}-2t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(4) = -(1)/(12)*(1 + t - 3*(t)^(2)- 2*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(4) == -Divide[1,12]*(1 + t - 3*(t)^(2)- 2*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex9 3.4#Ex9] || <math qid="Q1196">B_{2}^{4} = -\tfrac{1}{12}(1+t-3t^{2}-2t^{3})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{4} = -\tfrac{1}{12}(1+t-3t^{2}-2t^{3})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(4) = -(1)/(12)*(1 + t - 3*(t)^(2)- 2*(t)^(3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(4) == -Divide[1,12]*(1 + t - 3*(t)^(2)- 2*(t)^(3))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex10 3.4#Ex10] || [[Item:Q1198|<math>B_{-2}^{5} = \tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{5} = \tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(5) = (1)/(120)*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(5) == Divide[1,120]*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex10 3.4#Ex10] || <math qid="Q1198">B_{-2}^{5} = \tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5t^{4})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{5} = \tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(5) = (1)/(120)*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(5) == Divide[1,120]*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex11 3.4#Ex11] || [[Item:Q1199|<math>B_{-1}^{5} = -\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{5} = -\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(5) = -(1)/(24)*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(5) == -Divide[1,24]*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex11 3.4#Ex11] || <math qid="Q1199">B_{-1}^{5} = -\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5t^{4})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{5} = -\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(5) = -(1)/(24)*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(5) == -Divide[1,24]*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex12 3.4#Ex12] || [[Item:Q1200|<math>B_{0}^{5} = -\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{5} = -\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(5) = -(1)/(12)*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(5) == -Divide[1,12]*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex12 3.4#Ex12] || <math qid="Q1200">B_{0}^{5} = -\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t^{4})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{5} = -\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(5) = -(1)/(12)*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(5) == -Divide[1,12]*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex13 3.4#Ex13] || [[Item:Q1201|<math>B_{1}^{5} = \tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{5} = \tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(5) = (1)/(12)*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(5) == Divide[1,12]*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex13 3.4#Ex13] || <math qid="Q1201">B_{1}^{5} = \tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^{4})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{5} = \tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(5) = (1)/(12)*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(5) == Divide[1,12]*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex14 3.4#Ex14] || [[Item:Q1202|<math>B_{2}^{5} = -\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{5} = -\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(5) = -(1)/(24)*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(5) == -Divide[1,24]*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex14 3.4#Ex14] || <math qid="Q1202">B_{2}^{5} = -\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{4})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{5} = -\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(5) = -(1)/(24)*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(5) == -Divide[1,24]*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex15 3.4#Ex15] || [[Item:Q1203|<math>B_{3}^{5} = \tfrac{1}{120}(4-15t^{2}+5t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{5} = \tfrac{1}{120}(4-15t^{2}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(5) = (1)/(120)*(4 - 15*(t)^(2)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(5) == Divide[1,120]*(4 - 15*(t)^(2)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex15 3.4#Ex15] || <math qid="Q1203">B_{3}^{5} = \tfrac{1}{120}(4-15t^{2}+5t^{4})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{5} = \tfrac{1}{120}(4-15t^{2}+5t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(5) = (1)/(120)*(4 - 15*(t)^(2)+ 5*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(5) == Divide[1,120]*(4 - 15*(t)^(2)+ 5*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex16 3.4#Ex16] || [[Item:Q1205|<math>B_{-3}^{6} = -\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+15t^{4}-6t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-3}^{6} = -\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+15t^{4}-6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 3])^(6) = -(1)/(720)*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 3])^(6) == -Divide[1,720]*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex16 3.4#Ex16] || <math qid="Q1205">B_{-3}^{6} = -\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+15t^{4}-6t^{5})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-3}^{6} = -\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+15t^{4}-6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 3])^(6) = -(1)/(720)*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 3])^(6) == -Divide[1,720]*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex17 3.4#Ex17] || [[Item:Q1206|<math>B_{-2}^{6} = \tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{6} = \tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(6) = (1)/(60)*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(6) == Divide[1,60]*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex17 3.4#Ex17] || <math qid="Q1206">B_{-2}^{6} = \tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{6} = \tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(6) = (1)/(60)*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(6) == Divide[1,60]*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex18 3.4#Ex18] || [[Item:Q1207|<math>B_{-1}^{6} = -\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+5t^{4}-6t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{6} = -\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+5t^{4}-6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(6) = -(1)/(48)*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(6) == -Divide[1,48]*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex18 3.4#Ex18] || <math qid="Q1207">B_{-1}^{6} = -\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+5t^{4}-6t^{5})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{6} = -\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+5t^{4}-6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(6) = -(1)/(48)*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(6) == -Divide[1,48]*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex19 3.4#Ex19] || [[Item:Q1208|<math>B_{0}^{6} = -\tfrac{1}{18}t(49-28t^{2}+3t^{4})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{6} = -\tfrac{1}{18}t(49-28t^{2}+3t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(6) = -(1)/(18)*t*(49 - 28*(t)^(2)+ 3*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(6) == -Divide[1,18]*t*(49 - 28*(t)^(2)+ 3*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex19 3.4#Ex19] || <math qid="Q1208">B_{0}^{6} = -\tfrac{1}{18}t(49-28t^{2}+3t^{4})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{6} = -\tfrac{1}{18}t(49-28t^{2}+3t^{4})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(6) = -(1)/(18)*t*(49 - 28*(t)^(2)+ 3*(t)^(4))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(6) == -Divide[1,18]*t*(49 - 28*(t)^(2)+ 3*(t)^(4))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex20 3.4#Ex20] || [[Item:Q1209|<math>B_{1}^{6} = \tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t^{4}+6t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{6} = \tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t^{4}+6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(6) = (1)/(48)*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(6) == Divide[1,48]*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex20 3.4#Ex20] || <math qid="Q1209">B_{1}^{6} = \tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t^{4}+6t^{5})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{6} = \tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t^{4}+6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(6) = (1)/(48)*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(6) == Divide[1,48]*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/3.4#Ex21 3.4#Ex21] || [[Item:Q1210|<math>B_{2}^{6} = -\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{6} = -\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(6) = -(1)/(60)*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(6) == -Divide[1,60]*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex21 3.4#Ex21] || <math qid="Q1210">B_{2}^{6} = -\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{6} = -\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(6) = -(1)/(60)*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(6) == -Divide[1,60]*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex22 3.4#Ex22] || [[Item:Q1211|<math>B_{3}^{6} = \tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15t^{4}+6t^{5})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{6} = \tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15t^{4}+6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(6) = (1)/(720)*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(6) == Divide[1,720]*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex22 3.4#Ex22] || <math qid="Q1211">B_{3}^{6} = \tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15t^{4}+6t^{5})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{6} = \tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15t^{4}+6t^{5})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(6) = (1)/(720)*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(6) == Divide[1,720]*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/3.4#Ex23 3.4#Ex23] || [[Item:Q1213|<math>B_{-3}^{7} = -\tfrac{1}{5040}(48-56t-168t^{2}+140t^{3}+35t^{4}-42t^{5}+7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-3}^{7} = -\tfrac{1}{5040}(48-56t-168t^{2}+140t^{3}+35t^{4}-42t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 3])^(7) = -(1)/(5040)*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 3])^(7) == -Divide[1,5040]*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex23 3.4#Ex23] || <math qid="Q1213">B_{-3}^{7} = -\tfrac{1}{5040}(48-56t-168t^{2}+140t^{3}+35t^{4}-42t^{5}+7t^{6})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-3}^{7} = -\tfrac{1}{5040}(48-56t-168t^{2}+140t^{3}+35t^{4}-42t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 3])^(7) = -(1)/(5040)*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 3])^(7) == -Divide[1,5040]*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex24 3.4#Ex24] || [[Item:Q1214|<math>B_{-2}^{7} = \tfrac{1}{720}(72-108t-213t^{2}+240t^{3}-10t^{4}-36t^{5}+7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{7} = \tfrac{1}{720}(72-108t-213t^{2}+240t^{3}-10t^{4}-36t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(7) = (1)/(720)*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(7) == Divide[1,720]*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex24 3.4#Ex24] || <math qid="Q1214">B_{-2}^{7} = \tfrac{1}{720}(72-108t-213t^{2}+240t^{3}-10t^{4}-36t^{5}+7t^{6})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-2}^{7} = \tfrac{1}{720}(72-108t-213t^{2}+240t^{3}-10t^{4}-36t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 2])^(7) = (1)/(720)*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 2])^(7) == Divide[1,720]*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex25 3.4#Ex25] || [[Item:Q1215|<math>B_{-1}^{7} = -\tfrac{1}{240}(144-360t-48t^{2}+260t^{3}-45t^{4}-30t^{5}+7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{7} = -\tfrac{1}{240}(144-360t-48t^{2}+260t^{3}-45t^{4}-30t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(7) = -(1)/(240)*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(7) == -Divide[1,240]*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex25 3.4#Ex25] || <math qid="Q1215">B_{-1}^{7} = -\tfrac{1}{240}(144-360t-48t^{2}+260t^{3}-45t^{4}-30t^{5}+7t^{6})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{-1}^{7} = -\tfrac{1}{240}(144-360t-48t^{2}+260t^{3}-45t^{4}-30t^{5}+7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[- 1])^(7) = -(1)/(240)*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, - 1])^(7) == -Divide[1,240]*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex26 3.4#Ex26] || [[Item:Q1216|<math>B_{0}^{7} = -\tfrac{1}{144}(36+392t-147t^{2}-224t^{3}+70t^{4}+24t^{5}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{7} = -\tfrac{1}{144}(36+392t-147t^{2}-224t^{3}+70t^{4}+24t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(7) = -(1)/(144)*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(7) == -Divide[1,144]*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex26 3.4#Ex26] || <math qid="Q1216">B_{0}^{7} = -\tfrac{1}{144}(36+392t-147t^{2}-224t^{3}+70t^{4}+24t^{5}-7t^{6})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{0}^{7} = -\tfrac{1}{144}(36+392t-147t^{2}-224t^{3}+70t^{4}+24t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[0])^(7) = -(1)/(144)*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 0])^(7) == -Divide[1,144]*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex27 3.4#Ex27] || [[Item:Q1217|<math>B_{1}^{7} = \tfrac{1}{144}(144+216t-264t^{2}-156t^{3}+85t^{4}+18t^{5}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{7} = \tfrac{1}{144}(144+216t-264t^{2}-156t^{3}+85t^{4}+18t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(7) = (1)/(144)*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(7) == Divide[1,144]*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex27 3.4#Ex27] || <math qid="Q1217">B_{1}^{7} = \tfrac{1}{144}(144+216t-264t^{2}-156t^{3}+85t^{4}+18t^{5}-7t^{6})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{1}^{7} = \tfrac{1}{144}(144+216t-264t^{2}-156t^{3}+85t^{4}+18t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[1])^(7) = (1)/(144)*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 1])^(7) == Divide[1,144]*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex28 3.4#Ex28] || [[Item:Q1218|<math>B_{2}^{7} = -\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}+90t^{4}+12t^{5}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{7} = -\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}+90t^{4}+12t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(7) = -(1)/(240)*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(7) == -Divide[1,240]*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex28 3.4#Ex28] || <math qid="Q1218">B_{2}^{7} = -\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}+90t^{4}+12t^{5}-7t^{6})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{2}^{7} = -\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}+90t^{4}+12t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[2])^(7) = -(1)/(240)*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 2])^(7) == -Divide[1,240]*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex29 3.4#Ex29] || [[Item:Q1219|<math>B_{3}^{7} = \tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+85t^{4}+6t^{5}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{7} = \tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+85t^{4}+6t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(7) = (1)/(720)*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(7) == Divide[1,720]*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex29 3.4#Ex29] || <math qid="Q1219">B_{3}^{7} = \tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+85t^{4}+6t^{5}-7t^{6})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{3}^{7} = \tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+85t^{4}+6t^{5}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[3])^(7) = (1)/(720)*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 3])^(7) == Divide[1,720]*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/3.4#Ex30 3.4#Ex30] || [[Item:Q1220|<math>B_{4}^{7} = -\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t^{6})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{4}^{7} = -\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[4])^(7) = -(1)/(5040)*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 4])^(7) == -Divide[1,5040]*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/3.4#Ex30 3.4#Ex30] || <math qid="Q1220">B_{4}^{7} = -\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t^{6})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>B_{4}^{7} = -\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t^{6})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(B[4])^(7) = -(1)/(5040)*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(Subscript[B, 4])^(7) == -Divide[1,5040]*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-  
|-  
| [https://dlmf.nist.gov/3.4.E19 3.4.E19] || [[Item:Q1223|<math>\frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(factorial(k)) = (1)/(2*Pi*(r)^(k))*int(exp(r*cos(theta))*cos(r*sin(theta)- k*theta), theta = 0..2*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,(k)!] == Divide[1,2*Pi*(r)^(k)]*Integrate[Exp[r*Cos[\[Theta]]]*Cos[r*Sin[\[Theta]]- k*\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.
| [https://dlmf.nist.gov/3.4.E19 3.4.E19] || <math qid="Q1223">\frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(1)/(factorial(k)) = (1)/(2*Pi*(r)^(k))*int(exp(r*cos(theta))*cos(r*sin(theta)- k*theta), theta = 0..2*Pi)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,(k)!] == Divide[1,2*Pi*(r)^(k)]*Integrate[Exp[r*Cos[\[Theta]]]*Cos[r*Sin[\[Theta]]- k*\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 18]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.
Test Values: {r = -1.5, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000000
Test Values: {r = -1.5, k = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000000
Test Values: {r = -1.5, k = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1666666667
Test Values: {r = -1.5, k = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1666666667

Latest revision as of 11:03, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
3.4#Ex1 B - 1 3 = - 1 6 ⁢ ( 2 - 6 ⁢ t + 3 ⁢ t 2 ) superscript subscript 𝐵 1 3 1 6 2 6 𝑡 3 superscript 𝑡 2 {\displaystyle{\displaystyle B_{-1}^{3}=-\tfrac{1}{6}(2-6t+3t^{2})}}
B_{-1}^{3} = -\tfrac{1}{6}(2-6t+3t^{2})		 

(B[- 1])^(3) = -(1)/(6)*(2 - 6*t + 3*(t)^(2))
 
(Subscript[B, - 1])^(3) == -Divide[1,6]*(2 - 6*t + 3*(t)^(2))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex2 B 0 3 = - 1 2 ⁢ ( 1 + 4 ⁢ t - 3 ⁢ t 2 ) superscript subscript 𝐵 0 3 1 2 1 4 𝑡 3 superscript 𝑡 2 {\displaystyle{\displaystyle B_{0}^{3}=-\tfrac{1}{2}(1+4t-3t^{2})}}
B_{0}^{3} = -\tfrac{1}{2}(1+4t-3t^{2})		 

(B[0])^(3) = -(1)/(2)*(1 + 4*t - 3*(t)^(2))
 
(Subscript[B, 0])^(3) == -Divide[1,2]*(1 + 4*t - 3*(t)^(2))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex3 B 1 3 = 1 2 ⁢ ( 2 + 2 ⁢ t - 3 ⁢ t 2 ) superscript subscript 𝐵 1 3 1 2 2 2 𝑡 3 superscript 𝑡 2 {\displaystyle{\displaystyle B_{1}^{3}=\tfrac{1}{2}(2+2t-3t^{2})}}
B_{1}^{3} = \tfrac{1}{2}(2+2t-3t^{2})		 

(B[1])^(3) = (1)/(2)*(2 + 2*t - 3*(t)^(2))
 
(Subscript[B, 1])^(3) == Divide[1,2]*(2 + 2*t - 3*(t)^(2))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex4 B 2 3 = - 1 6 ⁢ ( 1 - 3 ⁢ t 2 ) superscript subscript 𝐵 2 3 1 6 1 3 superscript 𝑡 2 {\displaystyle{\displaystyle B_{2}^{3}=-\tfrac{1}{6}(1-3t^{2})}}
B_{2}^{3} = -\tfrac{1}{6}(1-3t^{2})		 

(B[2])^(3) = -(1)/(6)*(1 - 3*(t)^(2))
 
(Subscript[B, 2])^(3) == -Divide[1,6]*(1 - 3*(t)^(2))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex5 B - 2 4 = 1 12 ⁢ ( 1 - t - 3 ⁢ t 2 + 2 ⁢ t 3 ) superscript subscript 𝐵 2 4 1 12 1 𝑡 3 superscript 𝑡 2 2 superscript 𝑡 3 {\displaystyle{\displaystyle B_{-2}^{4}=\tfrac{1}{12}(1-t-3t^{2}+2t^{3})}}
B_{-2}^{4} = \tfrac{1}{12}(1-t-3t^{2}+2t^{3})		 

(B[- 2])^(4) = (1)/(12)*(1 - t - 3*(t)^(2)+ 2*(t)^(3))
 
(Subscript[B, - 2])^(4) == Divide[1,12]*(1 - t - 3*(t)^(2)+ 2*(t)^(3))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex6 B - 1 4 = - 1 6 ⁢ ( 4 - 8 ⁢ t - 3 ⁢ t 2 + 4 ⁢ t 3 ) superscript subscript 𝐵 1 4 1 6 4 8 𝑡 3 superscript 𝑡 2 4 superscript 𝑡 3 {\displaystyle{\displaystyle B_{-1}^{4}=-\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})}}
B_{-1}^{4} = -\tfrac{1}{6}(4-8t-3t^{2}+4t^{3})		 

(B[- 1])^(4) = -(1)/(6)*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3))
 
(Subscript[B, - 1])^(4) == -Divide[1,6]*(4 - 8*t - 3*(t)^(2)+ 4*(t)^(3))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex7 B 0 4 = - 1 2 ⁢ t ⁢ ( 5 - 2 ⁢ t 2 ) superscript subscript 𝐵 0 4 1 2 𝑡 5 2 superscript 𝑡 2 {\displaystyle{\displaystyle B_{0}^{4}=-\tfrac{1}{2}t(5-2t^{2})}}
B_{0}^{4} = -\tfrac{1}{2}t(5-2t^{2})		 

(B[0])^(4) = -(1)/(2)*t*(5 - 2*(t)^(2))
 
(Subscript[B, 0])^(4) == -Divide[1,2]*t*(5 - 2*(t)^(2))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex8 B 1 4 = 1 6 ⁢ ( 4 + 8 ⁢ t - 3 ⁢ t 2 - 4 ⁢ t 3 ) superscript subscript 𝐵 1 4 1 6 4 8 𝑡 3 superscript 𝑡 2 4 superscript 𝑡 3 {\displaystyle{\displaystyle B_{1}^{4}=\tfrac{1}{6}(4+8t-3t^{2}-4t^{3})}}
B_{1}^{4} = \tfrac{1}{6}(4+8t-3t^{2}-4t^{3})		 

(B[1])^(4) = (1)/(6)*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3))
 
(Subscript[B, 1])^(4) == Divide[1,6]*(4 + 8*t - 3*(t)^(2)- 4*(t)^(3))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex9 B 2 4 = - 1 12 ⁢ ( 1 + t - 3 ⁢ t 2 - 2 ⁢ t 3 ) superscript subscript 𝐵 2 4 1 12 1 𝑡 3 superscript 𝑡 2 2 superscript 𝑡 3 {\displaystyle{\displaystyle B_{2}^{4}=-\tfrac{1}{12}(1+t-3t^{2}-2t^{3})}}
B_{2}^{4} = -\tfrac{1}{12}(1+t-3t^{2}-2t^{3})		 

(B[2])^(4) = -(1)/(12)*(1 + t - 3*(t)^(2)- 2*(t)^(3))
 
(Subscript[B, 2])^(4) == -Divide[1,12]*(1 + t - 3*(t)^(2)- 2*(t)^(3))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex10 B - 2 5 = 1 120 ⁢ ( 6 - 10 ⁢ t - 15 ⁢ t 2 + 20 ⁢ t 3 - 5 ⁢ t 4 ) superscript subscript 𝐵 2 5 1 120 6 10 𝑡 15 superscript 𝑡 2 20 superscript 𝑡 3 5 superscript 𝑡 4 {\displaystyle{\displaystyle B_{-2}^{5}=\tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5% t^{4})}}
B_{-2}^{5} = \tfrac{1}{120}(6-10t-15t^{2}+20t^{3}-5t^{4})		 

(B[- 2])^(5) = (1)/(120)*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4))
 
(Subscript[B, - 2])^(5) == Divide[1,120]*(6 - 10*t - 15*(t)^(2)+ 20*(t)^(3)- 5*(t)^(4))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex11 B - 1 5 = - 1 24 ⁢ ( 12 - 32 ⁢ t + 3 ⁢ t 2 + 16 ⁢ t 3 - 5 ⁢ t 4 ) superscript subscript 𝐵 1 5 1 24 12 32 𝑡 3 superscript 𝑡 2 16 superscript 𝑡 3 5 superscript 𝑡 4 {\displaystyle{\displaystyle B_{-1}^{5}=-\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5% t^{4})}}
B_{-1}^{5} = -\tfrac{1}{24}(12-32t+3t^{2}+16t^{3}-5t^{4})		 

(B[- 1])^(5) = -(1)/(24)*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4))
 
(Subscript[B, - 1])^(5) == -Divide[1,24]*(12 - 32*t + 3*(t)^(2)+ 16*(t)^(3)- 5*(t)^(4))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex12 B 0 5 = - 1 12 ⁢ ( 4 + 30 ⁢ t - 15 ⁢ t 2 - 12 ⁢ t 3 + 5 ⁢ t 4 ) superscript subscript 𝐵 0 5 1 12 4 30 𝑡 15 superscript 𝑡 2 12 superscript 𝑡 3 5 superscript 𝑡 4 {\displaystyle{\displaystyle B_{0}^{5}=-\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t% ^{4})}}
B_{0}^{5} = -\tfrac{1}{12}(4+30t-15t^{2}-12t^{3}+5t^{4})		 

(B[0])^(5) = -(1)/(12)*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4))
 
(Subscript[B, 0])^(5) == -Divide[1,12]*(4 + 30*t - 15*(t)^(2)- 12*(t)^(3)+ 5*(t)^(4))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex13 B 1 5 = 1 12 ⁢ ( 12 + 16 ⁢ t - 21 ⁢ t 2 - 8 ⁢ t 3 + 5 ⁢ t 4 ) superscript subscript 𝐵 1 5 1 12 12 16 𝑡 21 superscript 𝑡 2 8 superscript 𝑡 3 5 superscript 𝑡 4 {\displaystyle{\displaystyle B_{1}^{5}=\tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^% {4})}}
B_{1}^{5} = \tfrac{1}{12}(12+16t-21t^{2}-8t^{3}+5t^{4})		 

(B[1])^(5) = (1)/(12)*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4))
 
(Subscript[B, 1])^(5) == Divide[1,12]*(12 + 16*t - 21*(t)^(2)- 8*(t)^(3)+ 5*(t)^(4))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex14 B 2 5 = - 1 24 ⁢ ( 6 + 2 ⁢ t - 21 ⁢ t 2 - 4 ⁢ t 3 + 5 ⁢ t 4 ) superscript subscript 𝐵 2 5 1 24 6 2 𝑡 21 superscript 𝑡 2 4 superscript 𝑡 3 5 superscript 𝑡 4 {\displaystyle{\displaystyle B_{2}^{5}=-\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{% 4})}}
B_{2}^{5} = -\tfrac{1}{24}(6+2t-21t^{2}-4t^{3}+5t^{4})		 

(B[2])^(5) = -(1)/(24)*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4))
 
(Subscript[B, 2])^(5) == -Divide[1,24]*(6 + 2*t - 21*(t)^(2)- 4*(t)^(3)+ 5*(t)^(4))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex15 B 3 5 = 1 120 ⁢ ( 4 - 15 ⁢ t 2 + 5 ⁢ t 4 ) superscript subscript 𝐵 3 5 1 120 4 15 superscript 𝑡 2 5 superscript 𝑡 4 {\displaystyle{\displaystyle B_{3}^{5}=\tfrac{1}{120}(4-15t^{2}+5t^{4})}}
B_{3}^{5} = \tfrac{1}{120}(4-15t^{2}+5t^{4})		 

(B[3])^(5) = (1)/(120)*(4 - 15*(t)^(2)+ 5*(t)^(4))
 
(Subscript[B, 3])^(5) == Divide[1,120]*(4 - 15*(t)^(2)+ 5*(t)^(4))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex16 B - 3 6 = - 1 720 ⁢ ( 12 - 8 ⁢ t - 45 ⁢ t 2 + 20 ⁢ t 3 + 15 ⁢ t 4 - 6 ⁢ t 5 ) superscript subscript 𝐵 3 6 1 720 12 8 𝑡 45 superscript 𝑡 2 20 superscript 𝑡 3 15 superscript 𝑡 4 6 superscript 𝑡 5 {\displaystyle{\displaystyle B_{-3}^{6}=-\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+% 15t^{4}-6t^{5})}}
B_{-3}^{6} = -\tfrac{1}{720}(12-8t-45t^{2}+20t^{3}+15t^{4}-6t^{5})		 

(B[- 3])^(6) = -(1)/(720)*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5))
 
(Subscript[B, - 3])^(6) == -Divide[1,720]*(12 - 8*t - 45*(t)^(2)+ 20*(t)^(3)+ 15*(t)^(4)- 6*(t)^(5))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex17 B - 2 6 = 1 60 ⁢ ( 9 - 9 ⁢ t - 30 ⁢ t 2 + 20 ⁢ t 3 + 5 ⁢ t 4 - 3 ⁢ t 5 ) superscript subscript 𝐵 2 6 1 60 9 9 𝑡 30 superscript 𝑡 2 20 superscript 𝑡 3 5 superscript 𝑡 4 3 superscript 𝑡 5 {\displaystyle{\displaystyle B_{-2}^{6}=\tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^% {4}-3t^{5})}}
B_{-2}^{6} = \tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5})		 

(B[- 2])^(6) = (1)/(60)*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5))
 
(Subscript[B, - 2])^(6) == Divide[1,60]*(9 - 9*t - 30*(t)^(2)+ 20*(t)^(3)+ 5*(t)^(4)- 3*(t)^(5))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex18 B - 1 6 = - 1 48 ⁢ ( 36 - 72 ⁢ t - 39 ⁢ t 2 + 52 ⁢ t 3 + 5 ⁢ t 4 - 6 ⁢ t 5 ) superscript subscript 𝐵 1 6 1 48 36 72 𝑡 39 superscript 𝑡 2 52 superscript 𝑡 3 5 superscript 𝑡 4 6 superscript 𝑡 5 {\displaystyle{\displaystyle B_{-1}^{6}=-\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+% 5t^{4}-6t^{5})}}
B_{-1}^{6} = -\tfrac{1}{48}(36-72t-39t^{2}+52t^{3}+5t^{4}-6t^{5})		 

(B[- 1])^(6) = -(1)/(48)*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5))
 
(Subscript[B, - 1])^(6) == -Divide[1,48]*(36 - 72*t - 39*(t)^(2)+ 52*(t)^(3)+ 5*(t)^(4)- 6*(t)^(5))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex19 B 0 6 = - 1 18 ⁢ t ⁢ ( 49 - 28 ⁢ t 2 + 3 ⁢ t 4 ) superscript subscript 𝐵 0 6 1 18 𝑡 49 28 superscript 𝑡 2 3 superscript 𝑡 4 {\displaystyle{\displaystyle B_{0}^{6}=-\tfrac{1}{18}t(49-28t^{2}+3t^{4})}}
B_{0}^{6} = -\tfrac{1}{18}t(49-28t^{2}+3t^{4})		 

(B[0])^(6) = -(1)/(18)*t*(49 - 28*(t)^(2)+ 3*(t)^(4))
 
(Subscript[B, 0])^(6) == -Divide[1,18]*t*(49 - 28*(t)^(2)+ 3*(t)^(4))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex20 B 1 6 = 1 48 ⁢ ( 36 + 72 ⁢ t - 39 ⁢ t 2 - 52 ⁢ t 3 + 5 ⁢ t 4 + 6 ⁢ t 5 ) superscript subscript 𝐵 1 6 1 48 36 72 𝑡 39 superscript 𝑡 2 52 superscript 𝑡 3 5 superscript 𝑡 4 6 superscript 𝑡 5 {\displaystyle{\displaystyle B_{1}^{6}=\tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t% ^{4}+6t^{5})}}
B_{1}^{6} = \tfrac{1}{48}(36+72t-39t^{2}-52t^{3}+5t^{4}+6t^{5})		 

(B[1])^(6) = (1)/(48)*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5))
 
(Subscript[B, 1])^(6) == Divide[1,48]*(36 + 72*t - 39*(t)^(2)- 52*(t)^(3)+ 5*(t)^(4)+ 6*(t)^(5))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex21 B 2 6 = - 1 60 ⁢ ( 9 + 9 ⁢ t - 30 ⁢ t 2 - 20 ⁢ t 3 + 5 ⁢ t 4 + 3 ⁢ t 5 ) superscript subscript 𝐵 2 6 1 60 9 9 𝑡 30 superscript 𝑡 2 20 superscript 𝑡 3 5 superscript 𝑡 4 3 superscript 𝑡 5 {\displaystyle{\displaystyle B_{2}^{6}=-\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^% {4}+3t^{5})}}
B_{2}^{6} = -\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5})		 

(B[2])^(6) = -(1)/(60)*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5))
 
(Subscript[B, 2])^(6) == -Divide[1,60]*(9 + 9*t - 30*(t)^(2)- 20*(t)^(3)+ 5*(t)^(4)+ 3*(t)^(5))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex22 B 3 6 = 1 720 ⁢ ( 12 + 8 ⁢ t - 45 ⁢ t 2 - 20 ⁢ t 3 + 15 ⁢ t 4 + 6 ⁢ t 5 ) superscript subscript 𝐵 3 6 1 720 12 8 𝑡 45 superscript 𝑡 2 20 superscript 𝑡 3 15 superscript 𝑡 4 6 superscript 𝑡 5 {\displaystyle{\displaystyle B_{3}^{6}=\tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15% t^{4}+6t^{5})}}
B_{3}^{6} = \tfrac{1}{720}(12+8t-45t^{2}-20t^{3}+15t^{4}+6t^{5})		 

(B[3])^(6) = (1)/(720)*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5))
 
(Subscript[B, 3])^(6) == Divide[1,720]*(12 + 8*t - 45*(t)^(2)- 20*(t)^(3)+ 15*(t)^(4)+ 6*(t)^(5))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex23 B - 3 7 = - 1 5040 ⁢ ( 48 - 56 ⁢ t - 168 ⁢ t 2 + 140 ⁢ t 3 + 35 ⁢ t 4 - 42 ⁢ t 5 + 7 ⁢ t 6 ) superscript subscript 𝐵 3 7 1 5040 48 56 𝑡 168 superscript 𝑡 2 140 superscript 𝑡 3 35 superscript 𝑡 4 42 superscript 𝑡 5 7 superscript 𝑡 6 {\displaystyle{\displaystyle B_{-3}^{7}=-\tfrac{1}{5040}(48-56t-168t^{2}+140t^% {3}+35t^{4}-42t^{5}+7t^{6})}}
B_{-3}^{7} = -\tfrac{1}{5040}(48-56t-168t^{2}+140t^{3}+35t^{4}-42t^{5}+7t^{6})		 

(B[- 3])^(7) = -(1)/(5040)*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6))
 
(Subscript[B, - 3])^(7) == -Divide[1,5040]*(48 - 56*t - 168*(t)^(2)+ 140*(t)^(3)+ 35*(t)^(4)- 42*(t)^(5)+ 7*(t)^(6))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex24 B - 2 7 = 1 720 ⁢ ( 72 - 108 ⁢ t - 213 ⁢ t 2 + 240 ⁢ t 3 - 10 ⁢ t 4 - 36 ⁢ t 5 + 7 ⁢ t 6 ) superscript subscript 𝐵 2 7 1 720 72 108 𝑡 213 superscript 𝑡 2 240 superscript 𝑡 3 10 superscript 𝑡 4 36 superscript 𝑡 5 7 superscript 𝑡 6 {\displaystyle{\displaystyle B_{-2}^{7}=\tfrac{1}{720}(72-108t-213t^{2}+240t^{% 3}-10t^{4}-36t^{5}+7t^{6})}}
B_{-2}^{7} = \tfrac{1}{720}(72-108t-213t^{2}+240t^{3}-10t^{4}-36t^{5}+7t^{6})		 

(B[- 2])^(7) = (1)/(720)*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6))
 
(Subscript[B, - 2])^(7) == Divide[1,720]*(72 - 108*t - 213*(t)^(2)+ 240*(t)^(3)- 10*(t)^(4)- 36*(t)^(5)+ 7*(t)^(6))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex25 B - 1 7 = - 1 240 ⁢ ( 144 - 360 ⁢ t - 48 ⁢ t 2 + 260 ⁢ t 3 - 45 ⁢ t 4 - 30 ⁢ t 5 + 7 ⁢ t 6 ) superscript subscript 𝐵 1 7 1 240 144 360 𝑡 48 superscript 𝑡 2 260 superscript 𝑡 3 45 superscript 𝑡 4 30 superscript 𝑡 5 7 superscript 𝑡 6 {\displaystyle{\displaystyle B_{-1}^{7}=-\tfrac{1}{240}(144-360t-48t^{2}+260t^% {3}-45t^{4}-30t^{5}+7t^{6})}}
B_{-1}^{7} = -\tfrac{1}{240}(144-360t-48t^{2}+260t^{3}-45t^{4}-30t^{5}+7t^{6})		 

(B[- 1])^(7) = -(1)/(240)*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6))
 
(Subscript[B, - 1])^(7) == -Divide[1,240]*(144 - 360*t - 48*(t)^(2)+ 260*(t)^(3)- 45*(t)^(4)- 30*(t)^(5)+ 7*(t)^(6))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex26 B 0 7 = - 1 144 ⁢ ( 36 + 392 ⁢ t - 147 ⁢ t 2 - 224 ⁢ t 3 + 70 ⁢ t 4 + 24 ⁢ t 5 - 7 ⁢ t 6 ) superscript subscript 𝐵 0 7 1 144 36 392 𝑡 147 superscript 𝑡 2 224 superscript 𝑡 3 70 superscript 𝑡 4 24 superscript 𝑡 5 7 superscript 𝑡 6 {\displaystyle{\displaystyle B_{0}^{7}=-\tfrac{1}{144}(36+392t-147t^{2}-224t^{% 3}+70t^{4}+24t^{5}-7t^{6})}}
B_{0}^{7} = -\tfrac{1}{144}(36+392t-147t^{2}-224t^{3}+70t^{4}+24t^{5}-7t^{6})		 

(B[0])^(7) = -(1)/(144)*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6))
 
(Subscript[B, 0])^(7) == -Divide[1,144]*(36 + 392*t - 147*(t)^(2)- 224*(t)^(3)+ 70*(t)^(4)+ 24*(t)^(5)- 7*(t)^(6))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex27 B 1 7 = 1 144 ⁢ ( 144 + 216 ⁢ t - 264 ⁢ t 2 - 156 ⁢ t 3 + 85 ⁢ t 4 + 18 ⁢ t 5 - 7 ⁢ t 6 ) superscript subscript 𝐵 1 7 1 144 144 216 𝑡 264 superscript 𝑡 2 156 superscript 𝑡 3 85 superscript 𝑡 4 18 superscript 𝑡 5 7 superscript 𝑡 6 {\displaystyle{\displaystyle B_{1}^{7}=\tfrac{1}{144}(144+216t-264t^{2}-156t^{% 3}+85t^{4}+18t^{5}-7t^{6})}}
B_{1}^{7} = \tfrac{1}{144}(144+216t-264t^{2}-156t^{3}+85t^{4}+18t^{5}-7t^{6})		 

(B[1])^(7) = (1)/(144)*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6))
 
(Subscript[B, 1])^(7) == Divide[1,144]*(144 + 216*t - 264*(t)^(2)- 156*(t)^(3)+ 85*(t)^(4)+ 18*(t)^(5)- 7*(t)^(6))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex28 B 2 7 = - 1 240 ⁢ ( 72 + 36 ⁢ t - 267 ⁢ t 2 - 80 ⁢ t 3 + 90 ⁢ t 4 + 12 ⁢ t 5 - 7 ⁢ t 6 ) superscript subscript 𝐵 2 7 1 240 72 36 𝑡 267 superscript 𝑡 2 80 superscript 𝑡 3 90 superscript 𝑡 4 12 superscript 𝑡 5 7 superscript 𝑡 6 {\displaystyle{\displaystyle B_{2}^{7}=-\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}% +90t^{4}+12t^{5}-7t^{6})}}
B_{2}^{7} = -\tfrac{1}{240}(72+36t-267t^{2}-80t^{3}+90t^{4}+12t^{5}-7t^{6})		 

(B[2])^(7) = -(1)/(240)*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6))
 
(Subscript[B, 2])^(7) == -Divide[1,240]*(72 + 36*t - 267*(t)^(2)- 80*(t)^(3)+ 90*(t)^(4)+ 12*(t)^(5)- 7*(t)^(6))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex29 B 3 7 = 1 720 ⁢ ( 48 + 8 ⁢ t - 192 ⁢ t 2 - 20 ⁢ t 3 + 85 ⁢ t 4 + 6 ⁢ t 5 - 7 ⁢ t 6 ) superscript subscript 𝐵 3 7 1 720 48 8 𝑡 192 superscript 𝑡 2 20 superscript 𝑡 3 85 superscript 𝑡 4 6 superscript 𝑡 5 7 superscript 𝑡 6 {\displaystyle{\displaystyle B_{3}^{7}=\tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+8% 5t^{4}+6t^{5}-7t^{6})}}
B_{3}^{7} = \tfrac{1}{720}(48+8t-192t^{2}-20t^{3}+85t^{4}+6t^{5}-7t^{6})		 

(B[3])^(7) = (1)/(720)*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6))
 
(Subscript[B, 3])^(7) == Divide[1,720]*(48 + 8*t - 192*(t)^(2)- 20*(t)^(3)+ 85*(t)^(4)+ 6*(t)^(5)- 7*(t)^(6))
 Skipped - no semantic math Skipped - no semantic math - -
3.4#Ex30 B 4 7 = - 1 5040 ⁢ ( 36 - 147 ⁢ t 2 + 70 ⁢ t 4 - 7 ⁢ t 6 ) superscript subscript 𝐵 4 7 1 5040 36 147 superscript 𝑡 2 70 superscript 𝑡 4 7 superscript 𝑡 6 {\displaystyle{\displaystyle B_{4}^{7}=-\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t% ^{6})}}
B_{4}^{7} = -\tfrac{1}{5040}(36-147t^{2}+70t^{4}-7t^{6})		 

(B[4])^(7) = -(1)/(5040)*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6))
 
(Subscript[B, 4])^(7) == -Divide[1,5040]*(36 - 147*(t)^(2)+ 70*(t)^(4)- 7*(t)^(6))
 Skipped - no semantic math Skipped - no semantic math - -
3.4.E19 1 k ! = 1 2 ⁢ π ⁢ r k ⁢ ∫ 0 2 ⁢ π e r ⁢ cos ⁡ θ ⁢ cos ⁡ ( r ⁢ sin ⁡ θ - k ⁢ θ ) ⁢ d θ 1 𝑘 1 2 superscript 𝑟 𝑘 superscript subscript 0 2 superscript 𝑒 𝑟 𝜃 𝑟 𝜃 𝑘 𝜃 𝜃 {\displaystyle{\displaystyle\frac{1}{k!}=\frac{1}{2\pi r^{k}}\int_{0}^{2\pi}e^% {r\cos\theta}\cos\left(r\sin\theta-k\theta\right)\mathrm{d}\theta}}
\frac{1}{k!} = \frac{1}{2\cpi r^{k}}\int_{0}^{2\cpi}e^{r\cos@@{\theta}}\cos@{r\sin@@{\theta}-k\theta}\diff{\theta}		 

(1)/(factorial(k)) = (1)/(2*Pi*(r)^(k))*int(exp(r*cos(theta))*cos(r*sin(theta)- k*theta), theta = 0..2*Pi)

Divide[1,(k)!] == Divide[1,2*Pi*(r)^(k)]*Integrate[Exp[r*Cos[\[Theta]]]*Cos[r*Sin[\[Theta]]- k*\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None]
Failure Aborted
Failed [18 / 18]
Result: 1.
Test Values: {r = -1.5, k = 1}


Result: .5000000000
Test Values: {r = -1.5, k = 2}


Result: .1666666667
Test Values: {r = -1.5, k = 3}


Result: 1.
Test Values: {r = 1.5, k = 1}

... skip entries to safe data
 Skipped - Because timed out
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