30.16: Difference between revisions

Latest revision as of 12:11, 28 June 2021

DLMF	Formula	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
30.16#Ex1	${\displaystyle{\displaystyle A_{j,j}=(m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2% )(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}}}$ `A_{j,j} = (m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2)(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}`	A[j , j] = (m + 2j - 2)(m + 2j - 1)- 2(gamma)^(2)((m + 2j - 2)(m + 2j - 1)- 1 + (m)^(2))/((2m + 4j - 5)(2m + 4*j - 1))	Subscript[A, j , j] == (m + 2j - 2)(m + 2j - 1)- 2\[Gamma]^(2)Divide[(m + 2j - 2)(m + 2j - 1)- 1 + (m)^(2),(2m + 4j - 5)(2m + 4*j - 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex2	${\displaystyle{\displaystyle A_{j,j+1}=-\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+% 4j-1)(2m+4j+1)}}}$ `A_{j,j+1} = -\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+4j-1)(2m+4j+1)}`	A[j , j + 1] = - (gamma)^(2)((2m + 2j - 1)(2m + 2j))/((2m + 4j - 1)(2m + 4*j + 1))	Subscript[A, j , j + 1] == - \[Gamma]^(2)Divide[(2m + 2j - 1)(2m + 2j),(2m + 4j - 1)(2m + 4*j + 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex3	${\displaystyle{\displaystyle A_{j,j-1}=-\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7% )(2m+4j-5)}}}$ `A_{j,j-1} = -\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7)(2m+4j-5)}`	A[j , j - 1] = - (gamma)^(2)((2j - 3)(2j - 2))/((2m + 4j - 7)(2m + 4*j - 5))	Subscript[A, j , j - 1] == - \[Gamma]^(2)Divide[(2j - 3)(2j - 2),(2m + 4j - 7)(2m + 4*j - 5)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16.E2	${\displaystyle{\displaystyle\alpha_{j,d+1}\leq\alpha_{j,d}}}$ `\alpha_{j,d+1} \leq \alpha_{j,d}`	alpha[j , d + 1] <= alpha[j , d]	Subscript[\[Alpha], j , d + 1] <= Subscript[\[Alpha], j , d]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex4	${\displaystyle{\displaystyle\alpha_{2,2}=14.18833\;246}}$ `\alpha_{2,2} = 14.18833\;246`	alpha[2 , 2] = 14.18833246	Subscript[\[Alpha], 2 , 2] == 14.18833246	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex5	${\displaystyle{\displaystyle\alpha_{2,3}=13.98002\;013}}$ `\alpha_{2,3} = 13.98002\;013`	alpha[2 , 3] = 13.98002013	Subscript[\[Alpha], 2 , 3] == 13.98002013	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex6	${\displaystyle{\displaystyle\alpha_{2,4}=13.97907\;459}}$ `\alpha_{2,4} = 13.97907\;459`	alpha[2 , 4] = 13.97907459	Subscript[\[Alpha], 2 , 4] == 13.97907459	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex7	${\displaystyle{\displaystyle\alpha_{2,5}=13.97907\;345}}$ `\alpha_{2,5} = 13.97907\;345`	alpha[2 , 5] = 13.97907345	Subscript[\[Alpha], 2 , 5] == 13.97907345	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex8	${\displaystyle{\displaystyle\alpha_{2,6}=13.97907\;345}}$ `\alpha_{2,6} = 13.97907\;345`	alpha[2 , 6] = 13.97907345	Subscript[\[Alpha], 2 , 6] == 13.97907345	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex9	${\displaystyle{\displaystyle A_{j,j}=(m+2j-1)(m+2j)-2\gamma^{2}\\frac{(m+2j-1% )(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}}}$ `A_{j,j} = (m+2j-1)(m+2j)-2\gamma^{2}\\frac{(m+2j-1)(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}`	A[j , j] = (m + 2j - 1)(m + 2j)- 2(gamma)^(2)((m + 2j - 1)(m + 2j)- 1 + (m)^(2))/((2m + 4j - 3)(2m + 4*j + 1))	Subscript[A, j , j] == (m + 2j - 1)(m + 2j)- 2\[Gamma]^(2)Divide[(m + 2j - 1)(m + 2j)- 1 + (m)^(2),(2m + 4j - 3)(2m + 4*j + 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex10	${\displaystyle{\displaystyle A_{j,j+1}=-\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+% 4j+1)(2m+4j+3)}}}$ `A_{j,j+1} = -\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+4j+1)(2m+4j+3)}`	A[j , j + 1] = - (gamma)^(2)((2m + 2j)(2m + 2j + 1))/((2m + 4j + 1)(2m + 4*j + 3))	Subscript[A, j , j + 1] == - \[Gamma]^(2)Divide[(2m + 2j)(2m + 2j + 1),(2m + 4j + 1)(2m + 4*j + 3)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16#Ex11	${\displaystyle{\displaystyle A_{j,j-1}=-\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5% )(2m+4j-3)}}}$ `A_{j,j-1} = -\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5)(2m+4j-3)}`	A[j , j - 1] = - (gamma)^(2)((2j - 2)(2j - 1))/((2m + 4j - 5)(2m + 4*j - 3))	Subscript[A, j , j - 1] == - \[Gamma]^(2)Divide[(2j - 2)(2j - 1),(2m + 4j - 5)(2m + 4*j - 3)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.16.E7	${\displaystyle{\displaystyle\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+% 2j-2p)!}\frac{1}{2n+4j-4p+1}=\frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}}}$ `\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+2j-2p)!}\frac{1}{2n+4j-4p+1} = \frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}`	sum((exp(1)[j , d])^(2)(factorial(n + m + 2j - 2p))/(factorial(n - m + 2j - 2p))(1)/(2n + 4j - 4p + 1), j = 1..d) = (factorial(n + m))/(factorial(n - m))(1)/(2*n + 1)	Sum[(Subscript[E, j , d])^(2)Divide[(n + m + 2j - 2p)!,(n - m + 2j - 2p)!]Divide[1,2n + 4j - 4p + 1], {j, 1, d}, GenerateConditions->None] == Divide[(n + m)!,(n - m)!]Divide[1,2*n + 1]	Skipped - no semantic math	Skipped - no semantic math	-	-

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex1 30.16#Ex1] || [[Item:Q8959|<math>A_{j,j} = (m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2)(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j} = (m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2)(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j] = (m + 2*j - 2)*(m + 2*j - 1)- 2*(gamma)^(2)*((m + 2*j - 2)*(m + 2*j - 1)- 1 + (m)^(2))/((2*m + 4*j - 5)*(2*m + 4*j - 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j] == (m + 2*j - 2)*(m + 2*j - 1)- 2*\[Gamma]^(2)*Divide[(m + 2*j - 2)*(m + 2*j - 1)- 1 + (m)^(2),(2*m + 4*j - 5)*(2*m + 4*j - 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex1 30.16#Ex1] || <math qid="Q8959">A_{j,j} = (m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2)(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j} = (m+2j-2)(m+2j-1)-2\gamma^{2}\frac{(m+2j-2)(m+2j-1)-1+m^{2}}{(2m+4j-5)(2m+4j-1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j] = (m + 2*j - 2)*(m + 2*j - 1)- 2*(gamma)^(2)*((m + 2*j - 2)*(m + 2*j - 1)- 1 + (m)^(2))/((2*m + 4*j - 5)*(2*m + 4*j - 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j] == (m + 2*j - 2)*(m + 2*j - 1)- 2*\[Gamma]^(2)*Divide[(m + 2*j - 2)*(m + 2*j - 1)- 1 + (m)^(2),(2*m + 4*j - 5)*(2*m + 4*j - 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex2 30.16#Ex2] || [[Item:Q8960|<math>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+4j-1)(2m+4j+1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+4j-1)(2m+4j+1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j + 1] = - (gamma)^(2)*((2*m + 2*j - 1)*(2*m + 2*j))/((2*m + 4*j - 1)*(2*m + 4*j + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j + 1] == - \[Gamma]^(2)*Divide[(2*m + 2*j - 1)*(2*m + 2*j),(2*m + 4*j - 1)*(2*m + 4*j + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex2 30.16#Ex2] || <math qid="Q8960">A_{j,j+1} = -\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+4j-1)(2m+4j+1)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j-1)(2m+2j)}{(2m+4j-1)(2m+4j+1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j + 1] = - (gamma)^(2)*((2*m + 2*j - 1)*(2*m + 2*j))/((2*m + 4*j - 1)*(2*m + 4*j + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j + 1] == - \[Gamma]^(2)*Divide[(2*m + 2*j - 1)*(2*m + 2*j),(2*m + 4*j - 1)*(2*m + 4*j + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex3 30.16#Ex3] || [[Item:Q8961|<math>A_{j,j-1} = -\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7)(2m+4j-5)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j-1} = -\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7)(2m+4j-5)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j - 1] = - (gamma)^(2)*((2*j - 3)*(2*j - 2))/((2*m + 4*j - 7)*(2*m + 4*j - 5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j - 1] == - \[Gamma]^(2)*Divide[(2*j - 3)*(2*j - 2),(2*m + 4*j - 7)*(2*m + 4*j - 5)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex3 30.16#Ex3] || <math qid="Q8961">A_{j,j-1} = -\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7)(2m+4j-5)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j-1} = -\gamma^{2}\frac{(2j-3)(2j-2)}{(2m+4j-7)(2m+4j-5)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j - 1] = - (gamma)^(2)*((2*j - 3)*(2*j - 2))/((2*m + 4*j - 7)*(2*m + 4*j - 5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j - 1] == - \[Gamma]^(2)*Divide[(2*j - 3)*(2*j - 2),(2*m + 4*j - 7)*(2*m + 4*j - 5)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16.E2 30.16.E2] || [[Item:Q8962|<math>\alpha_{j,d+1} \leq \alpha_{j,d}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{j,d+1} \leq \alpha_{j,d}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[j , d + 1] <= alpha[j , d]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], j , d + 1] <= Subscript[\[Alpha], j , d]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16.E2 30.16.E2] || <math qid="Q8962">\alpha_{j,d+1} \leq \alpha_{j,d}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{j,d+1} \leq \alpha_{j,d}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[j , d + 1] <= alpha[j , d]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], j , d + 1] <= Subscript[\[Alpha], j , d]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex4 30.16#Ex4] || [[Item:Q8965|<math>\alpha_{2,2} = 14.18833\;246</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,2} = 14.18833\;246</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 2] = 14.18833246</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 2] == 14.18833246</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex4 30.16#Ex4] || <math qid="Q8965">\alpha_{2,2} = 14.18833\;246</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,2} = 14.18833\;246</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 2] = 14.18833246</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 2] == 14.18833246</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex5 30.16#Ex5] || [[Item:Q8966|<math>\alpha_{2,3} = 13.98002\;013</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,3} = 13.98002\;013</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 3] = 13.98002013</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 3] == 13.98002013</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex5 30.16#Ex5] || <math qid="Q8966">\alpha_{2,3} = 13.98002\;013</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,3} = 13.98002\;013</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 3] = 13.98002013</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 3] == 13.98002013</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex6 30.16#Ex6] || [[Item:Q8967|<math>\alpha_{2,4} = 13.97907\;459</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,4} = 13.97907\;459</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 4] = 13.97907459</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 4] == 13.97907459</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex6 30.16#Ex6] || <math qid="Q8967">\alpha_{2,4} = 13.97907\;459</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,4} = 13.97907\;459</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 4] = 13.97907459</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 4] == 13.97907459</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex7 30.16#Ex7] || [[Item:Q8968|<math>\alpha_{2,5} = 13.97907\;345</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,5} = 13.97907\;345</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 5] = 13.97907345</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 5] == 13.97907345</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex7 30.16#Ex7] || <math qid="Q8968">\alpha_{2,5} = 13.97907\;345</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,5} = 13.97907\;345</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 5] = 13.97907345</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 5] == 13.97907345</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex8 30.16#Ex8] || [[Item:Q8969|<math>\alpha_{2,6} = 13.97907\;345</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,6} = 13.97907\;345</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 6] = 13.97907345</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 6] == 13.97907345</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex8 30.16#Ex8] || <math qid="Q8969">\alpha_{2,6} = 13.97907\;345</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\alpha_{2,6} = 13.97907\;345</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">alpha[2 , 6] = 13.97907345</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[\[Alpha], 2 , 6] == 13.97907345</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex9 30.16#Ex9] || [[Item:Q8970|<math>A_{j,j} = (m+2j-1)(m+2j)-2\gamma^{2}\*\frac{(m+2j-1)(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j} = (m+2j-1)(m+2j)-2\gamma^{2}\*\frac{(m+2j-1)(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j] = (m + 2*j - 1)*(m + 2*j)- 2*(gamma)^(2)*((m + 2*j - 1)*(m + 2*j)- 1 + (m)^(2))/((2*m + 4*j - 3)*(2*m + 4*j + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j] == (m + 2*j - 1)*(m + 2*j)- 2*\[Gamma]^(2)*Divide[(m + 2*j - 1)*(m + 2*j)- 1 + (m)^(2),(2*m + 4*j - 3)*(2*m + 4*j + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex9 30.16#Ex9] || <math qid="Q8970">A_{j,j} = (m+2j-1)(m+2j)-2\gamma^{2}\*\frac{(m+2j-1)(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j} = (m+2j-1)(m+2j)-2\gamma^{2}\*\frac{(m+2j-1)(m+2j)-1+m^{2}}{(2m+4j-3)(2m+4j+1)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j] = (m + 2*j - 1)*(m + 2*j)- 2*(gamma)^(2)*((m + 2*j - 1)*(m + 2*j)- 1 + (m)^(2))/((2*m + 4*j - 3)*(2*m + 4*j + 1))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j] == (m + 2*j - 1)*(m + 2*j)- 2*\[Gamma]^(2)*Divide[(m + 2*j - 1)*(m + 2*j)- 1 + (m)^(2),(2*m + 4*j - 3)*(2*m + 4*j + 1)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex10 30.16#Ex10] || [[Item:Q8971|<math>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+4j+1)(2m+4j+3)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+4j+1)(2m+4j+3)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j + 1] = - (gamma)^(2)*((2*m + 2*j)*(2*m + 2*j + 1))/((2*m + 4*j + 1)*(2*m + 4*j + 3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j + 1] == - \[Gamma]^(2)*Divide[(2*m + 2*j)*(2*m + 2*j + 1),(2*m + 4*j + 1)*(2*m + 4*j + 3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex10 30.16#Ex10] || <math qid="Q8971">A_{j,j+1} = -\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+4j+1)(2m+4j+3)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j+1} = -\gamma^{2}\frac{(2m+2j)(2m+2j+1)}{(2m+4j+1)(2m+4j+3)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j + 1] = - (gamma)^(2)*((2*m + 2*j)*(2*m + 2*j + 1))/((2*m + 4*j + 1)*(2*m + 4*j + 3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j + 1] == - \[Gamma]^(2)*Divide[(2*m + 2*j)*(2*m + 2*j + 1),(2*m + 4*j + 1)*(2*m + 4*j + 3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16#Ex11 30.16#Ex11] || [[Item:Q8972|<math>A_{j,j-1} = -\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5)(2m+4j-3)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j-1} = -\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5)(2m+4j-3)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j - 1] = - (gamma)^(2)*((2*j - 2)*(2*j - 1))/((2*m + 4*j - 5)*(2*m + 4*j - 3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j - 1] == - \[Gamma]^(2)*Divide[(2*j - 2)*(2*j - 1),(2*m + 4*j - 5)*(2*m + 4*j - 3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16#Ex11 30.16#Ex11] || <math qid="Q8972">A_{j,j-1} = -\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5)(2m+4j-3)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{j,j-1} = -\gamma^{2}\frac{(2j-2)(2j-1)}{(2m+4j-5)(2m+4j-3)}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[j , j - 1] = - (gamma)^(2)*((2*j - 2)*(2*j - 1))/((2*m + 4*j - 5)*(2*m + 4*j - 3))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, j , j - 1] == - \[Gamma]^(2)*Divide[(2*j - 2)*(2*j - 1),(2*m + 4*j - 5)*(2*m + 4*j - 3)]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |- style="background: #dfe6e9;"
-| [https://dlmf.nist.gov/30.16.E7 30.16.E7] || [[Item:Q8973|<math>\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+2j-2p)!}\frac{1}{2n+4j-4p+1} = \frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+2j-2p)!}\frac{1}{2n+4j-4p+1} = \frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((exp(1)[j , d])^(2)*(factorial(n + m + 2*j - 2*p))/(factorial(n - m + 2*j - 2*p))*(1)/(2*n + 4*j - 4*p + 1), j = 1..d) = (factorial(n + m))/(factorial(n - m))*(1)/(2*n + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[E, j , d])^(2)*Divide[(n + m + 2*j - 2*p)!,(n - m + 2*j - 2*p)!]*Divide[1,2*n + 4*j - 4*p + 1], {j, 1, d}, GenerateConditions->None] == Divide[(n + m)!,(n - m)!]*Divide[1,2*n + 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
+| [https://dlmf.nist.gov/30.16.E7 30.16.E7] || <math qid="Q8973">\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+2j-2p)!}\frac{1}{2n+4j-4p+1} = \frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+2j-2p)!}\frac{1}{2n+4j-4p+1} = \frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">sum((exp(1)[j , d])^(2)*(factorial(n + m + 2*j - 2*p))/(factorial(n - m + 2*j - 2*p))*(1)/(2*n + 4*j - 4*p + 1), j = 1..d) = (factorial(n + m))/(factorial(n - m))*(1)/(2*n + 1)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Sum[(Subscript[E, j , d])^(2)*Divide[(n + m + 2*j - 2*p)!,(n - m + 2*j - 2*p)!]*Divide[1,2*n + 4*j - 4*p + 1], {j, 1, d}, GenerateConditions->None] == Divide[(n + m)!,(n - m)!]*Divide[1,2*n + 1]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
 |}
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30.16: Difference between revisions

Latest revision as of 12:11, 28 June 2021

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