23.10: 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/23.10.E15 23.10.E15] || [[Item:Q7313|<math>A_{n} = \left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right)^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp@{-\frac{(n-1)\eta_{1}}{3\omega_{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}\right)}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{n} = \left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right)^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp@{-\frac{(n-1)\eta_{1}}{3\omega_{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}\right)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[n] = (((Pi)^(2)* (G)^(2))/(omega[1]))^((n)^(2)- 1)*((q)^(n*(n - 1)/2))/((I)^(n - 1))*exp(-((n - 1)*eta[1])/(3*omega[1])*((2*n - 1)*((omega[1])^(2)+ (omega[3])^(2))+ 3*(n - 1)*omega[1]*omega[3]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, n] == (Divide[(Pi)^(2)* (G)^(2),Subscript[\[Omega], 1]])^((n)^(2)- 1)*Divide[(q)^(n*(n - 1)/2),(I)^(n - 1)]*Exp[-Divide[(n - 1)*Subscript[\[Eta], 1],3*Subscript[\[Omega], 1]]*((2*n - 1)*((Subscript[\[Omega], 1])^(2)+ (Subscript[\[Omega], 3])^(2))+ 3*(n - 1)*Subscript[\[Omega], 1]*Subscript[\[Omega], 3])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1339745960+.5000000000*I
| [https://dlmf.nist.gov/23.10.E15 23.10.E15] || <math qid="Q7313">A_{n} = \left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right)^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp@{-\frac{(n-1)\eta_{1}}{3\omega_{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}\right)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>A_{n} = \left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right)^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp@{-\frac{(n-1)\eta_{1}}{3\omega_{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}\right)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>A[n] = (((Pi)^(2)* (G)^(2))/(omega[1]))^((n)^(2)- 1)*((q)^(n*(n - 1)/2))/((I)^(n - 1))*exp(-((n - 1)*eta[1])/(3*omega[1])*((2*n - 1)*((omega[1])^(2)+ (omega[3])^(2))+ 3*(n - 1)*omega[1]*omega[3]))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[A, n] == (Divide[(Pi)^(2)* (G)^(2),Subscript[\[Omega], 1]])^((n)^(2)- 1)*Divide[(q)^(n*(n - 1)/2),(I)^(n - 1)]*Exp[-Divide[(n - 1)*Subscript[\[Eta], 1],3*Subscript[\[Omega], 1]]*((2*n - 1)*((Subscript[\[Omega], 1])^(2)+ (Subscript[\[Omega], 3])^(2))+ 3*(n - 1)*Subscript[\[Omega], 1]*Subscript[\[Omega], 3])]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.1339745960+.5000000000*I
Test Values: {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.057001493+.6153915143*I
Test Values: {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.057001493+.6153915143*I
Test Values: {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
Test Values: {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
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| [https://dlmf.nist.gov/23.10#Ex1 23.10#Ex1] || [[Item:Q7314|<math>q = e^{\pi i\omega_{3}/\omega_{1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>q = e^{\pi i\omega_{3}/\omega_{1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q = exp(Pi*I*omega[3]/omega[1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q == Exp[Pi*I*Subscript[\[Omega], 3]/Subscript[\[Omega], 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/23.10#Ex1 23.10#Ex1] || <math qid="Q7314">q = e^{\pi i\omega_{3}/\omega_{1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>q = e^{\pi i\omega_{3}/\omega_{1}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q = exp(Pi*I*omega[3]/omega[1])</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">q == Exp[Pi*I*Subscript[\[Omega], 3]/Subscript[\[Omega], 1]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/23.10#Ex2 23.10#Ex2] || [[Item:Q7315|<math>G = \prod_{n=1}^{\infty}(1-q^{2n})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>G = \prod_{n=1}^{\infty}(1-q^{2n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">G = product(1 - (q)^(2*n), n = 1..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">G == Product[1 - (q)^(2*n), {n, 1, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/23.10#Ex2 23.10#Ex2] || <math qid="Q7315">G = \prod_{n=1}^{\infty}(1-q^{2n})</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>G = \prod_{n=1}^{\infty}(1-q^{2n})</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">G = product(1 - (q)^(2*n), n = 1..infinity)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">G == Product[1 - (q)^(2*n), {n, 1, Infinity}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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Latest revision as of 12:00, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
23.10.E15 A n = ( π 2 ⁢ G 2 ω 1 ) n 2 - 1 ⁢ q n ⁢ ( n - 1 ) / 2 i n - 1 ⁢ exp ⁡ ( - ( n - 1 ) ⁢ η 1 3 ⁢ ω 1 ⁢ ( ( 2 ⁢ n - 1 ) ⁢ ( ω 1 2 + ω 3 2 ) + 3 ⁢ ( n - 1 ) ⁢ ω 1 ⁢ ω 3 ) ) subscript 𝐴 𝑛 superscript superscript 𝜋 2 superscript 𝐺 2 subscript 𝜔 1 superscript 𝑛 2 1 superscript 𝑞 𝑛 𝑛 1 2 superscript 𝑖 𝑛 1 𝑛 1 subscript 𝜂 1 3 subscript 𝜔 1 2 𝑛 1 superscript subscript 𝜔 1 2 superscript subscript 𝜔 3 2 3 𝑛 1 subscript 𝜔 1 subscript 𝜔 3 {\displaystyle{\displaystyle A_{n}=\left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right% )^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp\left(-\frac{(n-1)\eta_{1}}{3\omega% _{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}% \right)\right)}}
A_{n} = \left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right)^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp@{-\frac{(n-1)\eta_{1}}{3\omega_{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}\right)}		 

A[n] = (((Pi)^(2)* (G)^(2))/(omega[1]))^((n)^(2)- 1)*((q)^(n*(n - 1)/2))/((I)^(n - 1))*exp(-((n - 1)*eta[1])/(3*omega[1])*((2*n - 1)*((omega[1])^(2)+ (omega[3])^(2))+ 3*(n - 1)*omega[1]*omega[3]))

Subscript[A, n] == (Divide[(Pi)^(2)* (G)^(2),Subscript[\[Omega], 1]])^((n)^(2)- 1)*Divide[(q)^(n*(n - 1)/2),(I)^(n - 1)]*Exp[-Divide[(n - 1)*Subscript[\[Eta], 1],3*Subscript[\[Omega], 1]]*((2*n - 1)*((Subscript[\[Omega], 1])^(2)+ (Subscript[\[Omega], 3])^(2))+ 3*(n - 1)*Subscript[\[Omega], 1]*Subscript[\[Omega], 3])]
Failure Failure
Failed [300 / 300]
Result: -.1339745960+.5000000000*I
Test Values: {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 1}


Result: 1.057001493+.6153915143*I
Test Values: {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 2}

... skip entries to safe data
 Skipped - Because timed out
23.10#Ex1 q = e π ⁢ i ⁢ ω 3 / ω 1 𝑞 superscript 𝑒 𝜋 𝑖 subscript 𝜔 3 subscript 𝜔 1 {\displaystyle{\displaystyle q=e^{\pi i\omega_{3}/\omega_{1}}}}
q = e^{\pi i\omega_{3}/\omega_{1}}		 

q = exp(Pi*I*omega[3]/omega[1])
 
q == Exp[Pi*I*Subscript[\[Omega], 3]/Subscript[\[Omega], 1]]
 Skipped - no semantic math Skipped - no semantic math - -
23.10#Ex2 G = ∏ n = 1 ∞ ( 1 - q 2 ⁢ n ) 𝐺 superscript subscript product 𝑛 1 1 superscript 𝑞 2 𝑛 {\displaystyle{\displaystyle G=\prod_{n=1}^{\infty}(1-q^{2n})}}
G = \prod_{n=1}^{\infty}(1-q^{2n})		 

G = product(1 - (q)^(2*n), n = 1..infinity)
 
G == Product[1 - (q)^(2*n), {n, 1, Infinity}, GenerateConditions->None]
 Skipped - no semantic math Skipped - no semantic math - -
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