View source for 10.11

{{DISPLAYTITLE:Bessel Functions - 10.11 Analytic Continuation}}

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! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/10.11.E1 10.11.E1] || [[Item:Q3103|<math>\BesselJ{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\BesselJ{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselJ{\nu}@{ze^{m\pi i}} = e^{m\nu\pi i}\BesselJ{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselJ(nu, z*exp(m*Pi*I)) = exp(m*nu*Pi*I)*BesselJ(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselJ[\[Nu], z*Exp[m*Pi*I]] == Exp[m*\[Nu]*Pi*I]*BesselJ[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [132 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.978604450-.5916012221*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4256613630-.5580360922e-1*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.9786044502778974, -0.5916012230349773]
Test Values: {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.42566136315461117, -0.05580360945599949]
Test Values: {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/10.11.E2 10.11.E2] || [[Item:Q3104|<math>\BesselY{\nu}@{ze^{m\pi i}} = e^{-m\nu\pi i}\BesselY{\nu}@{z}+2i\sin@{m\nu\pi}\cot@{\nu\pi}\BesselJ{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselY{\nu}@{ze^{m\pi i}} = e^{-m\nu\pi i}\BesselY{\nu}@{z}+2i\sin@{m\nu\pi}\cot@{\nu\pi}\BesselJ{\nu}@{z}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselY(nu, z*exp(m*Pi*I)) = exp(- m*nu*Pi*I)*BesselY(nu, z)+ 2*I*sin(m*nu*Pi)*cot(nu*Pi)*BesselJ(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselY[\[Nu], z*Exp[m*Pi*I]] == Exp[- m*\[Nu]*Pi*I]*BesselY[\[Nu], z]+ 2*I*Sin[m*\[Nu]*Pi]*Cot[\[Nu]*Pi]*BesselJ[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [170 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -4.492502702+3.271310776*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 19.72399963+2.416868418*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [162 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-4.49250270148862, 3.2713107749000305]
Test Values: {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[19.723999620348792, 2.416868461226219]
Test Values: {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/10.11.E3 10.11.E3] || [[Item:Q3105|<math>\sin@{\nu\pi}\HankelH{1}{\nu}@{ze^{m\pi i}} = -\sin@{(m-1)\nu\pi}\HankelH{1}{\nu}@{z}-e^{-\nu\pi i}\sin@{m\nu\pi}\HankelH{2}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{\nu\pi}\HankelH{1}{\nu}@{ze^{m\pi i}} = -\sin@{(m-1)\nu\pi}\HankelH{1}{\nu}@{z}-e^{-\nu\pi i}\sin@{m\nu\pi}\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(nu*Pi)*HankelH1(nu, z*exp(m*Pi*I)) = - sin((m - 1)*nu*Pi)*HankelH1(nu, z)- exp(- nu*Pi*I)*sin(m*nu*Pi)*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[\[Nu]*Pi]*HankelH1[\[Nu], z*Exp[m*Pi*I]] == - Sin[(m - 1)*\[Nu]*Pi]*HankelH1[\[Nu], z]- Exp[- \[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [132 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -16.06107638+5.815014709*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 39.27071892+24.34608468*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-16.061076381218605, 5.815014694873561]
Test Values: {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[39.27071883811536, 24.346084784539414]
Test Values: {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/10.11.E4 10.11.E4] || [[Item:Q3106|<math>\sin@{\nu\pi}\HankelH{2}{\nu}@{ze^{m\pi i}} = e^{\nu\pi i}\sin@{m\nu\pi}\HankelH{1}{\nu}@{z}+\sin@{(m+1)\nu\pi}\HankelH{2}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{\nu\pi}\HankelH{2}{\nu}@{ze^{m\pi i}} = e^{\nu\pi i}\sin@{m\nu\pi}\HankelH{1}{\nu}@{z}+\sin@{(m+1)\nu\pi}\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(nu*Pi)*HankelH2(nu, z*exp(m*Pi*I)) = exp(nu*Pi*I)*sin(m*nu*Pi)*HankelH1(nu, z)+ sin((m + 1)*nu*Pi)*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[\[Nu]*Pi]*HankelH2[\[Nu], z*Exp[m*Pi*I]] == Exp[\[Nu]*Pi*I]*Sin[m*\[Nu]*Pi]*HankelH1[\[Nu], z]+ Sin[(m + 1)*\[Nu]*Pi]*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [132 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 9.518923666+1.283901315*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -38.63237633-26.24866521*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [120 / 210]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[9.518923662743454, 1.2839013369012835]
Test Values: {Rule[m, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-38.63237622058036, -26.24866530437453]
Test Values: {Rule[m, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/10.11#Ex1 10.11#Ex1] || [[Item:Q3107|<math>\HankelH{1}{\nu}@{ze^{\pi i}} = -e^{-\nu\pi i}\HankelH{2}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HankelH{1}{\nu}@{ze^{\pi i}} = -e^{-\nu\pi i}\HankelH{2}{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>HankelH1(nu, z*exp(Pi*I)) = - exp(- nu*Pi*I)*HankelH2(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>HankelH1[\[Nu], z*Exp[Pi*I]] == - Exp[- \[Nu]*Pi*I]*HankelH2[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -5.249915228-5.084103922*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -3.129030441-5.176244122*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-5.2499152251779275, -5.084103924523598]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.4609763579335797, 35.01102127779514]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/10.11#Ex2 10.11#Ex2] || [[Item:Q3108|<math>\HankelH{2}{\nu}@{ze^{-\pi i}} = -e^{\nu\pi i}\HankelH{1}{\nu}@{z}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HankelH{2}{\nu}@{ze^{-\pi i}} = -e^{\nu\pi i}\HankelH{1}{\nu}@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>HankelH2(nu, z*exp(- Pi*I)) = - exp(nu*Pi*I)*HankelH1(nu, z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>HankelH2[\[Nu], z*Exp[- Pi*I]] == - Exp[\[Nu]*Pi*I]*HankelH1[\[Nu], z]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [50 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.033334476+.7163604616*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, z = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.427918302+.5187414665*I
Test Values: {nu = 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 [50 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.0333344760783634, 0.7163604618419928]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.538721989873022, -0.29666827540401164]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/10.11.E6 10.11.E6] || [[Item:Q3109|<math>\BesselY{n}@{ze^{m\pi i}} = (-1)^{mn}(\BesselY{n}@{z}+2im\BesselJ{n}@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BesselY{n}@{ze^{m\pi i}} = (-1)^{mn}(\BesselY{n}@{z}+2im\BesselJ{n}@{z})</syntaxhighlight> || <math>\realpart@@{(n+k+1)} > 0, \realpart@@{((-n)+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>BesselY(n, z*exp(m*Pi*I)) = (- 1)^(m*n)*(BesselY(n, z)+ 2*I*m*BesselJ(n, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BesselY[n, z*Exp[m*Pi*I]] == (- 1)^(m*n)*(BesselY[n, z]+ 2*I*m*BesselJ[n, z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [57 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.7553141392+1.723217630*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3969469092-.2695422112*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [48 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.7553141389736522, 1.7232176296930342]
Test Values: {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.39694690825884216, -0.26954221211204654]
Test Values: {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/10.11.E7 10.11.E7] || [[Item:Q3110|<math>\HankelH{1}{n}@{ze^{m\pi i}} = (-1)^{mn-1}((m-1)\HankelH{1}{n}@{z}+m\HankelH{2}{n}@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HankelH{1}{n}@{ze^{m\pi i}} = (-1)^{mn-1}((m-1)\HankelH{1}{n}@{z}+m\HankelH{2}{n}@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>HankelH1(n, z*exp(m*Pi*I)) = (- 1)^(m*n - 1)*((m - 1)*HankelH1(n, z)+ m*HankelH2(n, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HankelH1[n, z*Exp[m*Pi*I]] == (- 1)^(m*n - 1)*((m - 1)*HankelH1[n, z]+ m*HankelH2[n, z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [57 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.723217630-.7553141394*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .2695422111+.3969469092*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [48 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.7232176296930342, -0.7553141389736522]
Test Values: {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.26954221211204654, 0.39694690825884216]
Test Values: {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/10.11.E8 10.11.E8] || [[Item:Q3111|<math>\HankelH{2}{n}@{ze^{m\pi i}} = (-1)^{mn}(m\HankelH{1}{n}@{z}+(m+1)\HankelH{2}{n}@{z})</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\HankelH{2}{n}@{ze^{m\pi i}} = (-1)^{mn}(m\HankelH{1}{n}@{z}+(m+1)\HankelH{2}{n}@{z})</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>HankelH2(n, z*exp(m*Pi*I)) = (- 1)^(m*n)*(m*HankelH1(n, z)+(m + 1)*HankelH2(n, z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>HankelH2[n, z*Exp[m*Pi*I]] == (- 1)^(m*n)*(m*HankelH1[n, z]+(m + 1)*HankelH2[n, z])</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [57 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.723217630+.755314139*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.269542211-.396946909*I
Test Values: {z = 1/2*3^(1/2)+1/2*I, m = 1, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [48 / 63]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.7232176296930342, 0.7553141389736524]
Test Values: {Rule[m, 1], Rule[n, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.26954221211204654, -0.39694690825884216]
Test Values: {Rule[m, 1], Rule[n, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/10.11#E9X 10.11#E9X] || [[Item:Q3113|<math>\displaystyle\BesselJ{\nu}@{\conj{z}} = \conj{\BesselJ{\nu}@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\BesselJ{\nu}@{\conj{z}} = \conj{\BesselJ{\nu}@{z}}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">BesselJ(nu, conjugate(z)) = conjugate(BesselJ(nu, z))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">BesselJ[\[Nu], Conjugate[z]] == Conjugate[BesselJ[\[Nu], z]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/10.11#E9X 10.11#E9X] || [[Item:Q3113|<math>\displaystyle\BesselY{\nu}@{\conj{z}} = \conj{\BesselY{\nu}@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\BesselY{\nu}@{\conj{z}} = \conj{\BesselY{\nu}@{z}}</syntaxhighlight> || <math>\realpart@@{(\nu+k+1)} > 0, \realpart@@{((-\nu)+k+1)} > 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">BesselY(nu, conjugate(z)) = conjugate(BesselY(nu, z))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">BesselY[\[Nu], Conjugate[z]] == Conjugate[BesselY[\[Nu], z]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/10.11#E9Xa 10.11#E9Xa] || [[Item:Q3115|<math>\displaystyle\HankelH{1}{\nu}@{\conj{z}} = \conj{\HankelH{2}{\nu}@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\HankelH{1}{\nu}@{\conj{z}} = \conj{\HankelH{2}{\nu}@{z}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">HankelH1(nu, conjugate(z)) = conjugate(HankelH2(nu, z))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">HankelH1[\[Nu], Conjugate[z]] == Conjugate[HankelH2[\[Nu], z]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/10.11#E9Xa 10.11#E9Xa] || [[Item:Q3115|<math>\displaystyle\HankelH{2}{\nu}@{\conj{z}} = \conj{\HankelH{1}{\nu}@{z}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\displaystyle\HankelH{2}{\nu}@{\conj{z}} = \conj{\HankelH{1}{\nu}@{z}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">HankelH2(nu, conjugate(z)) = conjugate(HankelH1(nu, z))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">HankelH2[\[Nu], Conjugate[z]] == Conjugate[HankelH1[\[Nu], z]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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