10.25: Difference between revisions

From testwiki
Jump to navigation Jump to search
VisualWikitext
 
 
Line 14: Line 14:
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-  
|-  
| [https://dlmf.nist.gov/10.25.E1 10.25.E1] || [[Item:Q3488|<math>z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(z)^(2)* diff(w, [z$(2)])+ z*diff(w, z)-((z)^(2)+ (nu)^(2))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(z)^(2)* D[w, {z, 2}]+ z*D[w, z]-((z)^(2)+ \[Nu]^(2))*w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [220 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6467477718e-9-2.000000002*I
| [https://dlmf.nist.gov/10.25.E1 10.25.E1] || <math qid="Q3488">z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(z)^(2)* diff(w, [z$(2)])+ z*diff(w, z)-((z)^(2)+ (nu)^(2))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>(z)^(2)* D[w, {z, 2}]+ z*D[w, z]-((z)^(2)+ \[Nu]^(2))*w == 0</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [220 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6467477718e-9-2.000000002*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8660254040e-9-2.000000001*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.8660254040e-9-2.000000001*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [264 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -2.0]
Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [264 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.0, -2.0]
Line 20: Line 20:
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/10.25.E2 10.25.E2] || [[Item:Q3489|<math>\modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = ((1)/(2)*z)^(nu)* sum((((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == (Divide[1,2]*z)^\[Nu]* Sum[Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
| [https://dlmf.nist.gov/10.25.E2 10.25.E2] || <math qid="Q3489">\modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = ((1)/(2)*z)^(nu)* sum((((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == (Divide[1,2]*z)^\[Nu]* Sum[Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70]
|}
|}
</div>
</div>

Latest revision as of 11:24, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
10.25.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0}
z^{2}\deriv[2]{w}{z}+z\deriv{w}{z}-(z^{2}+\nu^{2})w = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(z)^(2)* diff(w, [z$(2)])+ z*diff(w, z)-((z)^(2)+ (nu)^(2))*w = 0

(z)^(2)* D[w, {z, 2}]+ z*D[w, z]-((z)^(2)+ \[Nu]^(2))*w == 0
Failure Failure
Failed [220 / 300]
Result: -.6467477718e-9-2.000000002*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: -.8660254040e-9-2.000000001*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2*3^(1/2)-1/2*I}

... skip entries to safe data
Failed [264 / 300]
Result: Complex[0.0, -2.0]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.0, -2.0]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[-5, 6]], Pi]]]}

... skip entries to safe data
10.25.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}}
\modBesselI{\nu}@{z} = (\tfrac{1}{2}z)^{\nu}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{4}z^{2})^{k}}{k!\EulerGamma@{\nu+k+1}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\nu+k+1)} > 0} 
BesselI(nu, z) = ((1)/(2)*z)^(nu)* sum((((1)/(4)*(z)^(2))^(k))/(factorial(k)*GAMMA(nu + k + 1)), k = 0..infinity)

BesselI[\[Nu], z] == (Divide[1,2]*z)^\[Nu]* Sum[Divide[(Divide[1,4]*(z)^(2))^(k),(k)!*Gamma[\[Nu]+ k + 1]], {k, 0, Infinity}, GenerateConditions->None]
Successful Successful - Successful [Tested: 70]
Retrieved from "https://lct.wmflabs.org/w/index.php?title=10.25&oldid=58199"