28.7: 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/28.7.E1 28.7.E1] || [[Item:Q8261|<math>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuA(2*n, q)-(2*n)^(2), n = 0..infinity) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicA[2*n, q]-(2*n)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| [https://dlmf.nist.gov/28.7.E1 28.7.E1] || <math qid="Q8261">\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuA(2*n, q)-(2*n)^(2), n = 0..infinity) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicA[2*n, q]-(2*n)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.7.E2 28.7.E2] || [[Item:Q8262|<math>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuA(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = q</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicA[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == q</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| [https://dlmf.nist.gov/28.7.E2 28.7.E2] || <math qid="Q8262">\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuA(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = q</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicA[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == q</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.7.E3 28.7.E3] || [[Item:Q8263|<math>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuB(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = - q</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicB[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == - q</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| [https://dlmf.nist.gov/28.7.E3 28.7.E3] || <math qid="Q8263">\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuB(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = - q</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicB[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == - q</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
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| [https://dlmf.nist.gov/28.7.E4 28.7.E4] || [[Item:Q8264|<math>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuB(2*n + 2, q)-(2*n + 2)^(2), n = 0..infinity) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicB[2*n + 2, q]-(2*n + 2)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
| [https://dlmf.nist.gov/28.7.E4 28.7.E4] || <math qid="Q8264">\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(MathieuB(2*n + 2, q)-(2*n + 2)^(2), n = 0..infinity) = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[MathieuCharacteristicB[2*n + 2, q]-(2*n + 2)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || 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
28.7.E1 ∑ n = 0 ∞ ( a 2 ⁢ n ⁡ ( q ) - ( 2 ⁢ n ) 2 ) = 0 superscript subscript 𝑛 0 Mathieu-eigenvalue-a 2 𝑛 𝑞 superscript 2 𝑛 2 0 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\left(a_{2n}\left(q\right)-(2n)% ^{2}\right)=0}}
\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0		 

sum(MathieuA(2*n, q)-(2*n)^(2), n = 0..infinity) = 0

Sum[MathieuCharacteristicA[2*n, q]-(2*n)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0
Failure Failure Skipped - Because timed out Skipped - Because timed out
28.7.E2 ∑ n = 0 ∞ ( a 2 ⁢ n + 1 ⁡ ( q ) - ( 2 ⁢ n + 1 ) 2 ) = q superscript subscript 𝑛 0 Mathieu-eigenvalue-a 2 𝑛 1 𝑞 superscript 2 𝑛 1 2 𝑞 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\left(a_{2n+1}\left(q\right)-(2% n+1)^{2}\right)=q}}
\sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q		 

sum(MathieuA(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = q

Sum[MathieuCharacteristicA[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == q
Failure Failure Skipped - Because timed out Skipped - Because timed out
28.7.E3 ∑ n = 0 ∞ ( b 2 ⁢ n + 1 ⁡ ( q ) - ( 2 ⁢ n + 1 ) 2 ) = - q superscript subscript 𝑛 0 Mathieu-eigenvalue-b 2 𝑛 1 𝑞 superscript 2 𝑛 1 2 𝑞 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\left(b_{2n+1}\left(q\right)-(2% n+1)^{2}\right)=-q}}
\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q		 

sum(MathieuB(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = - q

Sum[MathieuCharacteristicB[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == - q
Failure Failure Skipped - Because timed out Skipped - Because timed out
28.7.E4 ∑ n = 0 ∞ ( b 2 ⁢ n + 2 ⁡ ( q ) - ( 2 ⁢ n + 2 ) 2 ) = 0 superscript subscript 𝑛 0 Mathieu-eigenvalue-b 2 𝑛 2 𝑞 superscript 2 𝑛 2 2 0 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}\left(b_{2n+2}\left(q\right)-(2% n+2)^{2}\right)=0}}
\sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0		 

sum(MathieuB(2*n + 2, q)-(2*n + 2)^(2), n = 0..infinity) = 0

Sum[MathieuCharacteristicB[2*n + 2, q]-(2*n + 2)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0
Failure Failure Skipped - Because timed out Skipped - Because timed out
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