28.8: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/28.8#Ex3 28.8#Ex3] || [[Item:Q8273|<math>\dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(MathieuCE(m, (h)^(2), x))/(MathieuCE(m, (h)^(2), 0)) = ((2)^(m -((1)/(2))))/(sigma[m])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))+ (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[MathieuC[m, (h)^(2), x],MathieuC[m, (h)^(2), 0]] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Sigma], m]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])+ (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))</syntaxhighlight> || Error || Failure || - || Skipped - Because timed out
| [https://dlmf.nist.gov/28.8#Ex3 28.8#Ex3] || <math qid="Q8273">\dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(MathieuCE(m, (h)^(2), x))/(MathieuCE(m, (h)^(2), 0)) = ((2)^(m -((1)/(2))))/(sigma[m])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))+ (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[MathieuC[m, (h)^(2), x],MathieuC[m, (h)^(2), 0]] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Sigma], m]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])+ (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))</syntaxhighlight> || Error || Failure || - || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.8#Ex4 28.8#Ex4] || [[Item:Q8274|<math>\dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(MathieuSE(m + 1, (h)^(2), x))/(subs( temp=0, diff( MathieuSE(m + 1, (h)^(2), temp), temp$(1) ) )) = ((2)^(m -((1)/(2))))/(tau[m + 1])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))- (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[MathieuS[m + 1, (h)^(2), x],D[MathieuS[m + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Tau], m + 1]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])- (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))</syntaxhighlight> || Error || Failure || - || Skipped - Because timed out
| [https://dlmf.nist.gov/28.8#Ex4 28.8#Ex4] || <math qid="Q8274">\dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(MathieuSE(m + 1, (h)^(2), x))/(subs( temp=0, diff( MathieuSE(m + 1, (h)^(2), temp), temp$(1) ) )) = ((2)^(m -((1)/(2))))/(tau[m + 1])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))- (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[MathieuS[m + 1, (h)^(2), x],D[MathieuS[m + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Tau], m + 1]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])- (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))</syntaxhighlight> || Error || Failure || - || Skipped - Because timed out
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Latest revision as of 12:07, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
28.8#Ex3 ce m ⁡ ( x , h 2 ) ce m ⁡ ( 0 , h 2 ) = 2 m - ( 1 / 2 ) σ m ⁢ ( W m + ⁢ ( x ) ⁢ ( P m ⁢ ( x ) - Q m ⁢ ( x ) ) + W m - ⁢ ( x ) ⁢ ( P m ⁢ ( x ) + Q m ⁢ ( x ) ) ) Mathieu-ce 𝑚 𝑥 superscript ℎ 2 Mathieu-ce 𝑚 0 superscript ℎ 2 superscript 2 𝑚 1 2 subscript 𝜎 𝑚 superscript subscript 𝑊 𝑚 𝑥 subscript 𝑃 𝑚 𝑥 subscript 𝑄 𝑚 𝑥 superscript subscript 𝑊 𝑚 𝑥 subscript 𝑃 𝑚 𝑥 subscript 𝑄 𝑚 𝑥 {\displaystyle{\displaystyle\dfrac{\mathrm{ce}_{m}\left(x,h^{2}\right)}{% \mathrm{ce}_{m}\left(0,h^{2}\right)}=\dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}% \left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)}}
\dfrac{\Mathieuce{m}@{x}{h^{2}}}{\Mathieuce{m}@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\sigma_{m}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))+W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)		 

(MathieuCE(m, (h)^(2), x))/(MathieuCE(m, (h)^(2), 0)) = ((2)^(m -((1)/(2))))/(sigma[m])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))+ (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))

Divide[MathieuC[m, (h)^(2), x],MathieuC[m, (h)^(2), 0]] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Sigma], m]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])+ (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))
Error Failure - Skipped - Because timed out
28.8#Ex4 se m + 1 ⁡ ( x , h 2 ) se m + 1 ′ ⁡ ( 0 , h 2 ) = 2 m - ( 1 / 2 ) τ m + 1 ⁢ ( W m + ⁢ ( x ) ⁢ ( P m ⁢ ( x ) - Q m ⁢ ( x ) ) - W m - ⁢ ( x ) ⁢ ( P m ⁢ ( x ) + Q m ⁢ ( x ) ) ) Mathieu-se 𝑚 1 𝑥 superscript ℎ 2 diffop Mathieu-se 𝑚 1 1 0 superscript ℎ 2 superscript 2 𝑚 1 2 subscript 𝜏 𝑚 1 superscript subscript 𝑊 𝑚 𝑥 subscript 𝑃 𝑚 𝑥 subscript 𝑄 𝑚 𝑥 superscript subscript 𝑊 𝑚 𝑥 subscript 𝑃 𝑚 𝑥 subscript 𝑄 𝑚 𝑥 {\displaystyle{\displaystyle\dfrac{\mathrm{se}_{m+1}\left(x,h^{2}\right)}{% \mathrm{se}_{m+1}'\left(0,h^{2}\right)}=\dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1% }}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)}}
\dfrac{\Mathieuse{m+1}@{x}{h^{2}}}{\Mathieuse{m+1}'@{0}{h^{2}}} = \dfrac{2^{m-(\ifrac{1}{2})}}{\tau_{m+1}}\left(W_{m}^{+}(x)(P_{m}(x)-Q_{m}(x))-W_{m}^{-}(x)(P_{m}(x)+Q_{m}(x))\right)		 

(MathieuSE(m + 1, (h)^(2), x))/(subs( temp=0, diff( MathieuSE(m + 1, (h)^(2), temp), temp$(1) ) )) = ((2)^(m -((1)/(2))))/(tau[m + 1])*((W[m])^(+)(x)*(P[m](x)- Q[m](x))- (W[m])^(-)(x)*(P[m](x)+ Q[m](x)))

Divide[MathieuS[m + 1, (h)^(2), x],D[MathieuS[m + 1, (h)^(2), temp], {temp, 1}]/.temp-> 0] == Divide[(2)^(m -(Divide[1,2])),Subscript[\[Tau], m + 1]]*((Subscript[W, m])^(+)[x]*(Subscript[P, m][x]- Subscript[Q, m][x])- (Subscript[W, m])^(-)[x]*(Subscript[P, m][x]+ Subscript[Q, m][x]))
Error Failure - Skipped - Because timed out
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