27.13: 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/27.13.E4 27.13.E4] || [[Item:Q8096|<math>\AThetaFunction@{x} = 1+2\sum_{m=1}^{\infty}x^{m^{2}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AThetaFunction@{x} = 1+2\sum_{m=1}^{\infty}x^{m^{2}}</syntaxhighlight> || <math>|x| < 1</math> || <syntaxhighlight lang=mathematica>1+2*(sum((x)^(m^2), m = 1 .. infinity)) = 1 + 2*sum((x)^((m)^(2)), m = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
| [https://dlmf.nist.gov/27.13.E4 27.13.E4] || <math qid="Q8096">\AThetaFunction@{x} = 1+2\sum_{m=1}^{\infty}x^{m^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\AThetaFunction@{x} = 1+2\sum_{m=1}^{\infty}x^{m^{2}}</syntaxhighlight> || <math>|x| < 1</math> || <syntaxhighlight lang=mathematica>1+2*(sum((x)^(m^2), m = 1 .. infinity)) = 1 + 2*sum((x)^((m)^(2)), m = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/27.13.E6 27.13.E6] || [[Item:Q8098|<math>(\AThetaFunction@{x})^{2} = 1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\AThetaFunction@{x})^{2} = 1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}</syntaxhighlight> || <math>|x| < 1</math> || <syntaxhighlight lang=mathematica>(1+2*(sum((x)^(m^2), m = 1 .. infinity)))^(2) = 1 + 4*sum((delta[1](n)- delta[3](n))*(x)^(n), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.532372013
| [https://dlmf.nist.gov/27.13.E6 27.13.E6] || <math qid="Q8098">(\AThetaFunction@{x})^{2} = 1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(\AThetaFunction@{x})^{2} = 1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}</syntaxhighlight> || <math>|x| < 1</math> || <syntaxhighlight lang=mathematica>(1+2*(sum((x)^(m^2), m = 1 .. infinity)))^(2) = 1 + 4*sum((delta[1](n)- delta[3](n))*(x)^(n), n = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.532372013
Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -7.395831219+2.928203232*I
Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -7.395831219+2.928203232*I
Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || -
Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || -
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Latest revision as of 12:06, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
27.13.E4 ϑ ⁡ ( x ) = 1 + 2 ⁢ ∑ m = 1 ∞ x m 2 a-theta-function 𝑥 1 2 superscript subscript 𝑚 1 superscript 𝑥 superscript 𝑚 2 {\displaystyle{\displaystyle\vartheta\left(x\right)=1+2\sum_{m=1}^{\infty}x^{m% ^{2}}}}
\AThetaFunction@{x} = 1+2\sum_{m=1}^{\infty}x^{m^{2}}		 | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}} 
1+2*(sum((x)^(m^2), m = 1 .. infinity)) = 1 + 2*sum((x)^((m)^(2)), m = 1..infinity)

Error
Successful Missing Macro Error - -
27.13.E6 ( ϑ ⁡ ( x ) ) 2 = 1 + 4 ⁢ ∑ n = 1 ∞ ( δ 1 ⁢ ( n ) - δ 3 ⁢ ( n ) ) ⁢ x n superscript a-theta-function 𝑥 2 1 4 superscript subscript 𝑛 1 subscript 𝛿 1 𝑛 subscript 𝛿 3 𝑛 superscript 𝑥 𝑛 {\displaystyle{\displaystyle(\vartheta\left(x\right))^{2}=1+4\sum_{n=1}^{% \infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}}}
(\AThetaFunction@{x})^{2} = 1+4\sum_{n=1}^{\infty}\left(\delta_{1}(n)-\delta_{3}(n)\right)x^{n}		 | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}} 
(1+2*(sum((x)^(m^2), m = 1 .. infinity)))^(2) = 1 + 4*sum((delta[1](n)- delta[3](n))*(x)^(n), n = 1..infinity)

Error
Failure Missing Macro Error
Failed [300 / 300]
Result: 3.532372013
Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = 1/2*3^(1/2)+1/2*I}


Result: -7.395831219+2.928203232*I
Test Values: {delta = 1/2*3^(1/2)+1/2*I, x = 1/2, delta[1] = 1/2*3^(1/2)+1/2*I, delta[3] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
 -
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