32.5: 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/32.5.E1 32.5.E1] || [[Item:Q9236|<math>K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>K(z , zeta) = k*AiryAi((z + zeta)/(2))+((k)^(2))/(4)* int(int(K(z , s)* AiryAi((s + t)/(2))*AiryAi((t + zeta)/(2)), s = z..infinity), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>K[z , \[Zeta]] == k*AiryAi[Divide[z + \[Zeta],2]]+Divide[(k)^(2),4]* Integrate[Integrate[K[z , s]* AiryAi[Divide[s + t,2]]*AiryAi[Divide[t + \[Zeta],2]], {s, z, Infinity}, GenerateConditions->None], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Error
| [https://dlmf.nist.gov/32.5.E1 32.5.E1] || <math qid="Q9236">K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>K(z , zeta) = k*AiryAi((z + zeta)/(2))+((k)^(2))/(4)* int(int(K(z , s)* AiryAi((s + t)/(2))*AiryAi((t + zeta)/(2)), s = z..infinity), t = z..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>K[z , \[Zeta]] == k*AiryAi[Divide[z + \[Zeta],2]]+Divide[(k)^(2),4]* Integrate[Integrate[K[z , s]* AiryAi[Divide[s + t,2]]*AiryAi[Divide[t + \[Zeta],2]], {s, z, Infinity}, GenerateConditions->None], {t, z, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Error
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| [https://dlmf.nist.gov/32.5.E2 32.5.E2] || [[Item:Q9237|<math>w(z) = K(z,z)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = K(z,z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = K(z , z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == K[z , z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/32.5.E2 32.5.E2] || <math qid="Q9237">w(z) = K(z,z)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>w(z) = K(z,z)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w(z) = K(z , z)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">w[z] == K[z , z]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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Latest revision as of 12:12, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
32.5.E1 K ⁢ ( z , ζ ) = k ⁢ Ai ⁡ ( z + ζ 2 ) + k 2 4 ⁢ ∫ z ∞ ∫ z ∞ K ⁢ ( z , s ) ⁢ Ai ⁡ ( s + t 2 ) ⁢ Ai ⁡ ( t + ζ 2 ) ⁢ d s ⁢ d t 𝐾 𝑧 𝜁 𝑘 Airy-Ai 𝑧 𝜁 2 superscript 𝑘 2 4 superscript subscript 𝑧 superscript subscript 𝑧 𝐾 𝑧 𝑠 Airy-Ai 𝑠 𝑡 2 Airy-Ai 𝑡 𝜁 2 𝑠 𝑡 {\displaystyle{\displaystyle K(z,\zeta)=k\mathrm{Ai}\left(\frac{z+\zeta}{2}% \right)+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\mathrm% {Ai}\left(\frac{s+t}{2}\right)\mathrm{Ai}\left(\frac{t+\zeta}{2}\right)\mathrm% {d}s\mathrm{d}t}}
K(z,\zeta) = k\AiryAi@{\frac{z+\zeta}{2}}+\frac{k^{2}}{4}\*\int_{z}^{\infty}\!\!\!\int_{z}^{\infty}K(z,s)\AiryAi@{\frac{s+t}{2}}\AiryAi@{\frac{t+\zeta}{2}}\diff{s}\diff{t}		 

K(z , zeta) = k*AiryAi((z + zeta)/(2))+((k)^(2))/(4)* int(int(K(z , s)* AiryAi((s + t)/(2))*AiryAi((t + zeta)/(2)), s = z..infinity), t = z..infinity)

K[z , \[Zeta]] == k*AiryAi[Divide[z + \[Zeta],2]]+Divide[(k)^(2),4]* Integrate[Integrate[K[z , s]* AiryAi[Divide[s + t,2]]*AiryAi[Divide[t + \[Zeta],2]], {s, z, Infinity}, GenerateConditions->None], {t, z, Infinity}, GenerateConditions->None]
Failure Failure Skipped - Because timed out Error
32.5.E2 w ⁢ ( z ) = K ⁢ ( z , z ) 𝑤 𝑧 𝐾 𝑧 𝑧 {\displaystyle{\displaystyle w(z)=K(z,z)}}
w(z) = K(z,z)		 

w(z) = K(z , z)
 
w[z] == K[z , z]
 Skipped - no semantic math Skipped - no semantic math - -
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