10.27: Difference between revisions
Jump to navigation
Jump to search
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
||
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/10.27.E1 10.27.E1] | | | [https://dlmf.nist.gov/10.27.E1 10.27.E1] || <math qid="Q3491">\modBesselI{-n}@{z} = \modBesselI{n}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{-n}@{z} = \modBesselI{n}@{z}</syntaxhighlight> || <math>\realpart@@{((-n)+k+1)} > 0, \realpart@@{(n+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(- n, z) = BesselI(n, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[- n, z] == BesselI[n, z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 21] || Successful [Tested: 21] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E2 10.27.E2] | | | [https://dlmf.nist.gov/10.27.E2 10.27.E2] || <math qid="Q3492">\modBesselI{-\nu}@{z} = \modBesselI{\nu}@{z}+(2/\pi)\sin@{\nu\pi}\modBesselK{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{-\nu}@{z} = \modBesselI{\nu}@{z}+(2/\pi)\sin@{\nu\pi}\modBesselK{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(- nu, z) = BesselI(nu, z)+(2/Pi)*sin(nu*Pi)*BesselK(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[- \[Nu], z] == BesselI[\[Nu], z]+(2/Pi)*Sin[\[Nu]*Pi]*BesselK[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E3 10.27.E3] | | | [https://dlmf.nist.gov/10.27.E3 10.27.E3] || <math qid="Q3493">\modBesselK{-\nu}@{z} = \modBesselK{\nu}@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{-\nu}@{z} = \modBesselK{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BesselK(- nu, z) = BesselK(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[- \[Nu], z] == BesselK[\[Nu], z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 70] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E4 10.27.E4] | | | [https://dlmf.nist.gov/10.27.E4 10.27.E4] || <math qid="Q3494">\modBesselK{\nu}@{z} = \tfrac{1}{2}\pi\frac{\modBesselI{-\nu}@{z}-\modBesselI{\nu}@{z}}{\sin@{\nu\pi}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselK{\nu}@{z} = \tfrac{1}{2}\pi\frac{\modBesselI{-\nu}@{z}-\modBesselI{\nu}@{z}}{\sin@{\nu\pi}}</syntaxhighlight> || <math>\realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselK(nu, z) = (1)/(2)*Pi*(BesselI(- nu, z)- BesselI(nu, z))/(sin(nu*Pi))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselK[\[Nu], z] == Divide[1,2]*Pi*Divide[BesselI[- \[Nu], z]- BesselI[\[Nu], z],Sin[\[Nu]*Pi]]</syntaxhighlight> || Successful || Successful || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate | ||
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div> | Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div> | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E6 10.27.E6] | | | [https://dlmf.nist.gov/10.27.E6 10.27.E6] || <math qid="Q3496">\modBesselI{\nu}@{z} = e^{-\nu\pi i/2}\BesselJ{\nu}@{ze^{+\pi i/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = e^{-\nu\pi i/2}\BesselJ{\nu}@{ze^{+\pi i/2}}</syntaxhighlight> || <math>-\pi \leq +\phase@@{z}, -\pi \leq -\phase@@{z}, +\phase@@{z} \leq \tfrac{1}{2}\pi, -\phase@@{z} \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = exp(- nu*Pi*I/2)*BesselJ(nu, z*exp(+ Pi*I/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Exp[- \[Nu]*Pi*I/2]*BesselJ[\[Nu], z*Exp[+ Pi*I/2]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 50] || Successful [Tested: 50] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E6 10.27.E6] | | | [https://dlmf.nist.gov/10.27.E6 10.27.E6] || <math qid="Q3496">\modBesselI{\nu}@{z} = e^{+\nu\pi i/2}\BesselJ{\nu}@{ze^{-\pi i/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = e^{+\nu\pi i/2}\BesselJ{\nu}@{ze^{-\pi i/2}}</syntaxhighlight> || <math>-\pi \leq +\phase@@{z}, -\pi \leq -\phase@@{z}, +\phase@@{z} \leq \tfrac{1}{2}\pi, -\phase@@{z} \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = exp(+ nu*Pi*I/2)*BesselJ(nu, z*exp(- Pi*I/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Exp[+ \[Nu]*Pi*I/2]*BesselJ[\[Nu], z*Exp[- Pi*I/2]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 50] || Successful [Tested: 50] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E7 10.27.E7] | | | [https://dlmf.nist.gov/10.27.E7 10.27.E7] || <math qid="Q3497">\modBesselI{\nu}@{z} = \tfrac{1}{2}e^{-\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{+\pi i/2}}+\HankelH{2}{\nu}@{ze^{+\pi i/2}}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \tfrac{1}{2}e^{-\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{+\pi i/2}}+\HankelH{2}{\nu}@{ze^{+\pi i/2}}\right)</syntaxhighlight> || <math>-\pi \leq +\phase@@{z}, -\pi \leq -\phase@@{z}, +\phase@@{z} \leq \tfrac{1}{2}\pi, -\phase@@{z} \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (1)/(2)*exp(- nu*Pi*I/2)*(HankelH1(nu, z*exp(+ Pi*I/2))+ HankelH2(nu, z*exp(+ Pi*I/2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[1,2]*Exp[- \[Nu]*Pi*I/2]*(HankelH1[\[Nu], z*Exp[+ Pi*I/2]]+ HankelH2[\[Nu], z*Exp[+ Pi*I/2]])</syntaxhighlight> || Failure || Failure || Successful [Tested: 50] || Successful [Tested: 50] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E7 10.27.E7] | | | [https://dlmf.nist.gov/10.27.E7 10.27.E7] || <math qid="Q3497">\modBesselI{\nu}@{z} = \tfrac{1}{2}e^{+\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{-\pi i/2}}+\HankelH{2}{\nu}@{ze^{-\pi i/2}}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\modBesselI{\nu}@{z} = \tfrac{1}{2}e^{+\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{-\pi i/2}}+\HankelH{2}{\nu}@{ze^{-\pi i/2}}\right)</syntaxhighlight> || <math>-\pi \leq +\phase@@{z}, -\pi \leq -\phase@@{z}, +\phase@@{z} \leq \tfrac{1}{2}\pi, -\phase@@{z} \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselI(nu, z) = (1)/(2)*exp(+ nu*Pi*I/2)*(HankelH1(nu, z*exp(- Pi*I/2))+ HankelH2(nu, z*exp(- Pi*I/2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselI[\[Nu], z] == Divide[1,2]*Exp[+ \[Nu]*Pi*I/2]*(HankelH1[\[Nu], z*Exp[- Pi*I/2]]+ HankelH2[\[Nu], z*Exp[- Pi*I/2]])</syntaxhighlight> || Failure || Failure || Successful [Tested: 50] || Successful [Tested: 50] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E9 10.27.E9] | | | [https://dlmf.nist.gov/10.27.E9 10.27.E9] || <math qid="Q3499">\pi i\BesselJ{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}-e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\pi i\BesselJ{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}-e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}</syntaxhighlight> || <math>|\phase@@{z}| \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>Pi*I*BesselJ(nu, z) = exp(- nu*Pi*I/2)*BesselK(nu, z*exp(- Pi*I/2))- exp(nu*Pi*I/2)*BesselK(nu, z*exp(Pi*I/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Pi*I*BesselJ[\[Nu], z] == Exp[- \[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[- Pi*I/2]]- Exp[\[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[Pi*I/2]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 50] || Successful [Tested: 50] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E10 10.27.E10] | | | [https://dlmf.nist.gov/10.27.E10 10.27.E10] || <math qid="Q3500">-\pi\BesselY{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}+e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\pi\BesselY{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}+e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}</syntaxhighlight> || <math>|\phase@@{z}| \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>- Pi*BesselY(nu, z) = exp(- nu*Pi*I/2)*BesselK(nu, z*exp(- Pi*I/2))+ exp(nu*Pi*I/2)*BesselK(nu, z*exp(Pi*I/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>- Pi*BesselY[\[Nu], z] == Exp[- \[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[- Pi*I/2]]+ Exp[\[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[Pi*I/2]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 50] || Successful [Tested: 50] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E11 10.27.E11] | | | [https://dlmf.nist.gov/10.27.E11 10.27.E11] || <math qid="Q3501">\BesselY{\nu}@{z} = e^{+(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{-\pi i/2}}-(2/\pi)e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselY{\nu}@{z} = e^{+(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{-\pi i/2}}-(2/\pi)e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}</syntaxhighlight> || <math>-\tfrac{1}{2}\pi \leq +\phase@@{z}, -\tfrac{1}{2}\pi \leq -\phase@@{z}, +\phase@@{z} \leq \pi, -\phase@@{z} \leq \pi, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselY(nu, z) = exp(+(nu + 1)*Pi*I/2)*BesselI(nu, z*exp(- Pi*I/2))-(2/Pi)*exp(- nu*Pi*I/2)*BesselK(nu, z*exp(- Pi*I/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselY[\[Nu], z] == Exp[+(\[Nu]+ 1)*Pi*I/2]*BesselI[\[Nu], z*Exp[- Pi*I/2]]-(2/Pi)*Exp[- \[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[- Pi*I/2]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 50] || Successful [Tested: 50] | ||
|- | |- | ||
| [https://dlmf.nist.gov/10.27.E11 10.27.E11] | | | [https://dlmf.nist.gov/10.27.E11 10.27.E11] || <math qid="Q3501">\BesselY{\nu}@{z} = e^{-(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{+\pi i/2}}-(2/\pi)e^{+\nu\pi i/2}\modBesselK{\nu}@{ze^{+\pi i/2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselY{\nu}@{z} = e^{-(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{+\pi i/2}}-(2/\pi)e^{+\nu\pi i/2}\modBesselK{\nu}@{ze^{+\pi i/2}}</syntaxhighlight> || <math>-\tfrac{1}{2}\pi \leq +\phase@@{z}, -\tfrac{1}{2}\pi \leq -\phase@@{z}, +\phase@@{z} \leq \pi, -\phase@@{z} \leq \pi, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselY(nu, z) = exp(-(nu + 1)*Pi*I/2)*BesselI(nu, z*exp(+ Pi*I/2))-(2/Pi)*exp(+ nu*Pi*I/2)*BesselK(nu, z*exp(+ Pi*I/2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselY[\[Nu], z] == Exp[-(\[Nu]+ 1)*Pi*I/2]*BesselI[\[Nu], z*Exp[+ Pi*I/2]]-(2/Pi)*Exp[+ \[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[+ Pi*I/2]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 50] || Successful [Tested: 50] | ||
|} | |} | ||
</div> | </div> |
Latest revision as of 11:24, 28 June 2021
DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
---|---|---|---|---|---|---|---|---|
10.27.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-n}@{z} = \modBesselI{n}@{z}}
\modBesselI{-n}@{z} = \modBesselI{n}@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((-n)+k+1)} > 0, \realpart@@{(n+k+1)} > 0} | BesselI(- n, z) = BesselI(n, z)
|
BesselI[- n, z] == BesselI[n, z]
|
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
10.27.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{-\nu}@{z} = \modBesselI{\nu}@{z}+(2/\pi)\sin@{\nu\pi}\modBesselK{\nu}@{z}}
\modBesselI{-\nu}@{z} = \modBesselI{\nu}@{z}+(2/\pi)\sin@{\nu\pi}\modBesselK{\nu}@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(\nu+k+1)} > 0} | BesselI(- nu, z) = BesselI(nu, z)+(2/Pi)*sin(nu*Pi)*BesselK(nu, z)
|
BesselI[- \[Nu], z] == BesselI[\[Nu], z]+(2/Pi)*Sin[\[Nu]*Pi]*BesselK[\[Nu], z]
|
Successful | Successful | - | Successful [Tested: 70] |
10.27.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{-\nu}@{z} = \modBesselK{\nu}@{z}}
\modBesselK{-\nu}@{z} = \modBesselK{\nu}@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | BesselK(- nu, z) = BesselK(nu, z)
|
BesselK[- \[Nu], z] == BesselK[\[Nu], z]
|
Successful | Successful | - | Successful [Tested: 70] |
10.27.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z} = \tfrac{1}{2}\pi\frac{\modBesselI{-\nu}@{z}-\modBesselI{\nu}@{z}}{\sin@{\nu\pi}}}
\modBesselK{\nu}@{z} = \tfrac{1}{2}\pi\frac{\modBesselI{-\nu}@{z}-\modBesselI{\nu}@{z}}{\sin@{\nu\pi}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((-\nu)+k+1)} > 0, \realpart@@{(\nu+k+1)} > 0} | BesselK(nu, z) = (1)/(2)*Pi*(BesselI(- nu, z)- BesselI(nu, z))/(sin(nu*Pi))
|
BesselK[\[Nu], z] == Divide[1,2]*Pi*Divide[BesselI[- \[Nu], z]- BesselI[\[Nu], z],Sin[\[Nu]*Pi]]
|
Successful | Successful | - | Failed [14 / 70]
Result: Indeterminate
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, -2]}
Result: Indeterminate
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, 2]}
... skip entries to safe data |
10.27.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = e^{-\nu\pi i/2}\BesselJ{\nu}@{ze^{+\pi i/2}}}
\modBesselI{\nu}@{z} = e^{-\nu\pi i/2}\BesselJ{\nu}@{ze^{+\pi i/2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi \leq +\phase@@{z}, -\pi \leq -\phase@@{z}, +\phase@@{z} \leq \tfrac{1}{2}\pi, -\phase@@{z} \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0} | BesselI(nu, z) = exp(- nu*Pi*I/2)*BesselJ(nu, z*exp(+ Pi*I/2))
|
BesselI[\[Nu], z] == Exp[- \[Nu]*Pi*I/2]*BesselJ[\[Nu], z*Exp[+ Pi*I/2]]
|
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
10.27.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = e^{+\nu\pi i/2}\BesselJ{\nu}@{ze^{-\pi i/2}}}
\modBesselI{\nu}@{z} = e^{+\nu\pi i/2}\BesselJ{\nu}@{ze^{-\pi i/2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi \leq +\phase@@{z}, -\pi \leq -\phase@@{z}, +\phase@@{z} \leq \tfrac{1}{2}\pi, -\phase@@{z} \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0} | BesselI(nu, z) = exp(+ nu*Pi*I/2)*BesselJ(nu, z*exp(- Pi*I/2))
|
BesselI[\[Nu], z] == Exp[+ \[Nu]*Pi*I/2]*BesselJ[\[Nu], z*Exp[- Pi*I/2]]
|
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
10.27.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \tfrac{1}{2}e^{-\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{+\pi i/2}}+\HankelH{2}{\nu}@{ze^{+\pi i/2}}\right)}
\modBesselI{\nu}@{z} = \tfrac{1}{2}e^{-\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{+\pi i/2}}+\HankelH{2}{\nu}@{ze^{+\pi i/2}}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi \leq +\phase@@{z}, -\pi \leq -\phase@@{z}, +\phase@@{z} \leq \tfrac{1}{2}\pi, -\phase@@{z} \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0} | BesselI(nu, z) = (1)/(2)*exp(- nu*Pi*I/2)*(HankelH1(nu, z*exp(+ Pi*I/2))+ HankelH2(nu, z*exp(+ Pi*I/2)))
|
BesselI[\[Nu], z] == Divide[1,2]*Exp[- \[Nu]*Pi*I/2]*(HankelH1[\[Nu], z*Exp[+ Pi*I/2]]+ HankelH2[\[Nu], z*Exp[+ Pi*I/2]])
|
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
10.27.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselI{\nu}@{z} = \tfrac{1}{2}e^{+\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{-\pi i/2}}+\HankelH{2}{\nu}@{ze^{-\pi i/2}}\right)}
\modBesselI{\nu}@{z} = \tfrac{1}{2}e^{+\nu\pi i/2}\left(\HankelH{1}{\nu}@{ze^{-\pi i/2}}+\HankelH{2}{\nu}@{ze^{-\pi i/2}}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi \leq +\phase@@{z}, -\pi \leq -\phase@@{z}, +\phase@@{z} \leq \tfrac{1}{2}\pi, -\phase@@{z} \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0} | BesselI(nu, z) = (1)/(2)*exp(+ nu*Pi*I/2)*(HankelH1(nu, z*exp(- Pi*I/2))+ HankelH2(nu, z*exp(- Pi*I/2)))
|
BesselI[\[Nu], z] == Divide[1,2]*Exp[+ \[Nu]*Pi*I/2]*(HankelH1[\[Nu], z*Exp[- Pi*I/2]]+ HankelH2[\[Nu], z*Exp[- Pi*I/2]])
|
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
10.27.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi i\BesselJ{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}-e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}}
\pi i\BesselJ{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}-e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@@{z}| \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0} | Pi*I*BesselJ(nu, z) = exp(- nu*Pi*I/2)*BesselK(nu, z*exp(- Pi*I/2))- exp(nu*Pi*I/2)*BesselK(nu, z*exp(Pi*I/2))
|
Pi*I*BesselJ[\[Nu], z] == Exp[- \[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[- Pi*I/2]]- Exp[\[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[Pi*I/2]]
|
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
10.27.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\pi\BesselY{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}+e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}}}
-\pi\BesselY{\nu}@{z} = e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}+e^{\nu\pi i/2}\modBesselK{\nu}@{ze^{\pi i/2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@@{z}| \leq \tfrac{1}{2}\pi, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0} | - Pi*BesselY(nu, z) = exp(- nu*Pi*I/2)*BesselK(nu, z*exp(- Pi*I/2))+ exp(nu*Pi*I/2)*BesselK(nu, z*exp(Pi*I/2))
|
- Pi*BesselY[\[Nu], z] == Exp[- \[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[- Pi*I/2]]+ Exp[\[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[Pi*I/2]]
|
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
10.27.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = e^{+(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{-\pi i/2}}-(2/\pi)e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}}}
\BesselY{\nu}@{z} = e^{+(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{-\pi i/2}}-(2/\pi)e^{-\nu\pi i/2}\modBesselK{\nu}@{ze^{-\pi i/2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi \leq +\phase@@{z}, -\tfrac{1}{2}\pi \leq -\phase@@{z}, +\phase@@{z} \leq \pi, -\phase@@{z} \leq \pi, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0} | BesselY(nu, z) = exp(+(nu + 1)*Pi*I/2)*BesselI(nu, z*exp(- Pi*I/2))-(2/Pi)*exp(- nu*Pi*I/2)*BesselK(nu, z*exp(- Pi*I/2))
|
BesselY[\[Nu], z] == Exp[+(\[Nu]+ 1)*Pi*I/2]*BesselI[\[Nu], z*Exp[- Pi*I/2]]-(2/Pi)*Exp[- \[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[- Pi*I/2]]
|
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |
10.27.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselY{\nu}@{z} = e^{-(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{+\pi i/2}}-(2/\pi)e^{+\nu\pi i/2}\modBesselK{\nu}@{ze^{+\pi i/2}}}
\BesselY{\nu}@{z} = e^{-(\nu+1)\pi i/2}\modBesselI{\nu}@{ze^{+\pi i/2}}-(2/\pi)e^{+\nu\pi i/2}\modBesselK{\nu}@{ze^{+\pi i/2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\tfrac{1}{2}\pi \leq +\phase@@{z}, -\tfrac{1}{2}\pi \leq -\phase@@{z}, +\phase@@{z} \leq \pi, -\phase@@{z} \leq \pi, \realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0} | BesselY(nu, z) = exp(-(nu + 1)*Pi*I/2)*BesselI(nu, z*exp(+ Pi*I/2))-(2/Pi)*exp(+ nu*Pi*I/2)*BesselK(nu, z*exp(+ Pi*I/2))
|
BesselY[\[Nu], z] == Exp[-(\[Nu]+ 1)*Pi*I/2]*BesselI[\[Nu], z*Exp[+ Pi*I/2]]-(2/Pi)*Exp[+ \[Nu]*Pi*I/2]*BesselK[\[Nu], z*Exp[+ Pi*I/2]]
|
Failure | Failure | Successful [Tested: 50] | Successful [Tested: 50] |