Painlevé Transcendents - 32.10 Special Function Solutions

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
32.10.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = n+\tfrac{1}{2}}
\alpha = n+\tfrac{1}{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha = n +(1)/(2)
 
\[Alpha] == n +Divide[1,2]
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = C_{1}\AiryAi@{-2^{-1/3}z}+C_{2}\AiryBi@{-2^{-1/3}z}}
\phi(z) = C_{1}\AiryAi@{-2^{-1/3}z}+C_{2}\AiryBi@{-2^{-1/3}z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
phi(z) = C[1]*AiryAi(- (2)^(- 1/3)* z)+ C[2]*AiryBi(- (2)^(- 1/3)* z)

\[Phi][z] == Subscript[C, 1]*AiryAi[- (2)^(- 1/3)* z]+ Subscript[C, 2]*AiryBi[- (2)^(- 1/3)* z]
Failure Failure
Failed [300 / 300]
Result: -.2986692739+.5787509238*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}


Result: .3018910357e-1+.1740730853*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-0.29866927421000106, 0.5787509234724151]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.03018910341830547, 0.174073084997731]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
32.10.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;\tfrac{3}{2}) = \Phi-\dfrac{1}{2\Phi^{2}+z}}
w(z;\tfrac{3}{2}) = \Phi-\dfrac{1}{2\Phi^{2}+z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ;(3)/(2)) = Phi -(1)/(2*(Phi)^(2)+ z)
 
w[z ;Divide[3,2]] == \[CapitalPhi]-Divide[1,2*\[CapitalPhi]^(2)+ z]
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;\tfrac{5}{2}) = \dfrac{1}{2\Phi^{2}+z}+\dfrac{2z\Phi^{2}+\Phi+z^{2}}{4\Phi^{3}+2z\Phi-1}}
w(z;\tfrac{5}{2}) = \dfrac{1}{2\Phi^{2}+z}+\dfrac{2z\Phi^{2}+\Phi+z^{2}}{4\Phi^{3}+2z\Phi-1}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ;(5)/(2)) = (1)/(2*(Phi)^(2)+ z)+(2*z*(Phi)^(2)+ Phi + (z)^(2))/(4*(Phi)^(3)+ 2*z*Phi - 1)
 
w[z ;Divide[5,2]] == Divide[1,2*\[CapitalPhi]^(2)+ z]+Divide[2*z*\[CapitalPhi]^(2)+ \[CapitalPhi]+ (z)^(2),4*\[CapitalPhi]^(3)+ 2*z*\[CapitalPhi]- 1]
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;n+\tfrac{1}{2}) = \deriv{}{z}\left(\ln@{\frac{\tau_{n}(z)}{\tau_{n+1}(z)}}\right)}
w(z;n+\tfrac{1}{2}) = \deriv{}{z}\left(\ln@{\frac{\tau_{n}(z)}{\tau_{n+1}(z)}}\right)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; n +(1)/(2)) = diff(ln((tau[n](z))/(tau[n + 1](z))), z)

w[z ; n +Divide[1,2]] == D[Log[Divide[Subscript[\[Tau], n][z],Subscript[\[Tau], n + 1][z]]], z]
Translation Error Translation Error - -
32.10.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;-n-\tfrac{1}{2}) = -w(z;n+\tfrac{1}{2})}
w(z;-n-\tfrac{1}{2}) = -w(z;n+\tfrac{1}{2})		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; - n -(1)/(2)) = - w(z ; n +(1)/(2))
 
w[z ; - n -Divide[1,2]] == - w[z ; n +Divide[1,2]]
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{1}\alpha+\varepsilon_{2}\beta = 4n+2}
\varepsilon_{1}\alpha+\varepsilon_{2}\beta = 4n+2		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
varepsilon[1]*alpha + varepsilon[2]*beta = 4*n + 2
 
Subscript[\[CurlyEpsilon], 1]*\[Alpha]+ Subscript[\[CurlyEpsilon], 2]*\[Beta] == 4*n + 2
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = z^{\nu}\left(C_{1}\BesselJ{\nu}@{\zeta}+C_{2}\BesselY{\nu}@{\zeta}\right)}
\phi(z) = z^{\nu}\left(C_{1}\BesselJ{\nu}@{\zeta}+C_{2}\BesselY{\nu}@{\zeta}\right)		 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} 
phi(z) = (z)^(nu)*(C[1]*BesselJ(nu, zeta)+ C[2]*BesselY(nu, zeta))

\[Phi][z] == (z)^\[Nu]*(Subscript[C, 1]*BesselJ[\[Nu], \[Zeta]]+ Subscript[C, 2]*BesselY[\[Nu], \[Zeta]])
Failure Failure
Failed [300 / 300]
Result: .6857713611+1.049278090*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}


Result: -.1639325500+1.038275666*I
Test Values: {nu = 1/2*3^(1/2)+1/2*I, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[0.6857713606630202, 1.0492780901981935]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-0.16393255022963316, 1.0382756660889538]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
32.10.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = -2(2n+1+\varepsilon\alpha)^{2}}
\beta = -2(2n+1+\varepsilon\alpha)^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta = - 2*(2*n + 1 + varepsilon*alpha)^(2)
 
\[Beta] == - 2*(2*n + 1 + \[CurlyEpsilon]*\[Alpha])^(2)
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = -2n^{2}}
\beta = -2n^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta = - 2*(n)^(2)
 
\[Beta] == - 2*(n)^(2)
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = \left(C_{1}\paraU@{a}{\sqrt{2}z}+C_{2}\paraV@{a}{\sqrt{2}z}\right)\exp@{\tfrac{1}{2}\varepsilon z^{2}}}
\phi(z) = \left(C_{1}\paraU@{a}{\sqrt{2}z}+C_{2}\paraV@{a}{\sqrt{2}z}\right)\exp@{\tfrac{1}{2}\varepsilon z^{2}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
phi(z) = (C[1]*CylinderU(a, sqrt(2)*z)+ C[2]*CylinderV(a, sqrt(2)*z))*exp((1)/(2)*varepsilon*(z)^(2))

\[Phi][z] == (Subscript[C, 1]*ParabolicCylinderD[- 1/2 -(a), Sqrt[2]*z]+ Subscript[C, 2]*Divide[GAMMA[1/2 + a], Pi]*(Sin[Pi*(a)] * ParabolicCylinderD[-(a) - 1/2, Sqrt[2]*z] + ParabolicCylinderD[-(a) - 1/2, -(Sqrt[2]*z)]))*Exp[Divide[1,2]*\[CurlyEpsilon]*(z)^(2)]
Failure Failure
Failed [300 / 300]
Result: .6213533818-.8057984780*I
Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I, varepsilon = 1}


Result: 1.542195596-1.017130546*I
Test Values: {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I, varepsilon = 2}

... skip entries to safe data
Failed [300 / 300]
Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-1.165517214154348, -0.5387865015105858], Plus[Complex[0.9001043151387932, 0.6347232005321619], Times[Complex[-6.562724044143109*^-17, -2.768827103772538*^-17], GAMMA[-1.0]]]]]
Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Plus[Complex[0.5000000000000001, 0.8660254037844386], Times[Complex[-1.0681394822800956, -1.2559298845291706], Plus[Complex[0.9001043151387932, 0.6347232005321619], Times[Complex[-6.562724044143109*^-17, -2.768827103772538*^-17], GAMMA[-1.0]]]]]
Test Values: {Rule[a, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ε, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[C, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
32.10.E20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;-m,-2(m-1)^{2}) = -\frac{\HermitepolyH{m-1}'@{z}}{\HermitepolyH{m-1}@{z}}}
w(z;-m,-2(m-1)^{2}) = -\frac{\HermitepolyH{m-1}'@{z}}{\HermitepolyH{m-1}@{z}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; - m , - 2*(m - 1)^(2)) = -(diff( HermiteH(m - 1, z), z$(1) ))/(HermiteH(m - 1, z))

w[z ; - m , - 2*(m - 1)^(2)] == -Divide[D[HermiteH[m - 1, z], {z, 1}],HermiteH[m - 1, z]]
Translation Error Translation Error - -
32.10.E21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;-m,-2(m+1)^{2}) = -2z+\frac{\HermitepolyH{m}'@{z}}{\HermitepolyH{m}@{z}}}
w(z;-m,-2(m+1)^{2}) = -2z+\frac{\HermitepolyH{m}'@{z}}{\HermitepolyH{m}@{z}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; - m , - 2*(m + 1)^(2)) = - 2*z +(diff( HermiteH(m, z), z$(1) ))/(HermiteH(m, z))

w[z ; - m , - 2*(m + 1)^(2)] == - 2*z +Divide[D[HermiteH[m, z], {z, 1}],HermiteH[m, z]]
Translation Error Translation Error - -
32.10.E23 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a+b+\varepsilon_{3}\gamma = 2n+1}
a+b+\varepsilon_{3}\gamma = 2n+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
a + b + varepsilon[3]*gamma = 2*n + 1
 
a + b + Subscript[\[CurlyEpsilon], 3]*\[Gamma] == 2*n + 1
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E24 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (a-n)(b-n) = 0}
(a-n)(b-n) = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(a - n)*(b - n) = 0
 
(a - n)*(b - n) == 0
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E27 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(z) = \frac{C_{1}\WhittakerconfhyperM{\kappa}{\mu}@{\zeta}+C_{2}\WhittakerconfhyperW{\kappa}{\mu}@{\zeta}}{\zeta^{(a-b+1)/2}}\exp@{\tfrac{1}{2}\zeta}}
\phi(z) = \frac{C_{1}\WhittakerconfhyperM{\kappa}{\mu}@{\zeta}+C_{2}\WhittakerconfhyperW{\kappa}{\mu}@{\zeta}}{\zeta^{(a-b+1)/2}}\exp@{\tfrac{1}{2}\zeta}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
phi(z) = (C[1]*WhittakerM(kappa, mu, zeta)+ C[2]*WhittakerW(kappa, mu, zeta))/((zeta)^((a - b + 1)/2))*exp((1)/(2)*zeta)

\[Phi][z] == Divide[Subscript[C, 1]*WhittakerM[\[Kappa], \[Mu], \[Zeta]]+ Subscript[C, 2]*WhittakerW[\[Kappa], \[Mu], \[Zeta]],\[Zeta]^((a - b + 1)/2)]*Exp[Divide[1,2]*\[Zeta]]
Failure Failure Manual Skip! Skipped - Because timed out
32.10.E28 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a+b+c+d = 2n+1}
a+b+c+d = 2n+1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
a + b + c + d = 2*n + 1
 
a + b + c + d == 2*n + 1
 Skipped - no semantic math Skipped - no semantic math - -
32.10#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \frac{1}{1-z}}
\zeta = \frac{1}{1-z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
zeta = (1)/(1 - z)
 
\[Zeta] == Divide[1,1 - z]
 Skipped - no semantic math Skipped - no semantic math - -
32.10.E31 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi(\zeta) = C_{1}\hyperF@{b}{-a}{b+c}{\zeta}+C_{2}\zeta^{-b+1-c}\*\hyperF@{-a-b-c+1}{-c+1}{2-b-c}{\zeta}}
\phi(\zeta) = C_{1}\hyperF@{b}{-a}{b+c}{\zeta}+C_{2}\zeta^{-b+1-c}\*\hyperF@{-a-b-c+1}{-c+1}{2-b-c}{\zeta}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
phi(zeta) = C[1]*hypergeom([b, - a], [b + c], zeta)+ C[2]*(zeta)^(- b + 1 - c)* hypergeom([- a - b - c + 1, - c + 1], [2 - b - c], zeta)

\[Phi][\[Zeta]] == Subscript[C, 1]*Hypergeometric2F1[b, - a, b + c, \[Zeta]]+ Subscript[C, 2]*\[Zeta]^(- b + 1 - c)* Hypergeometric2F1[- a - b - c + 1, - c + 1, 2 - b - c, \[Zeta]]
Failure Failure
Failed [300 / 300]
Result: Float(infinity)+Float(infinity)*I
Test Values: {a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = 1/2*3^(1/2)+1/2*I}


Result: Float(infinity)+Float(infinity)*I
Test Values: {a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, zeta = 1/2*3^(1/2)+1/2*I, C[1] = 1/2*3^(1/2)+1/2*I, C[2] = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
 Skipped - Because timed out
32.10.E32 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u = \int_{0}^{\Lambda}\frac{\diff{t}}{\sqrt{t(t-1)(t-z)}}}
u = \int_{0}^{\Lambda}\frac{\diff{t}}{\sqrt{t(t-1)(t-z)}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
u = int((1)/(sqrt(t*(t - 1)*(t - z))), t = 0..Lambda)

u == Integrate[Divide[1,Sqrt[t*(t - 1)*(t - z)]], {t, 0, \[CapitalLambda]}, GenerateConditions->None]
Failure Aborted Skipped - Because timed out Skipped - Because timed out
32.10.E33 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(1-z)\deriv[2]{\phi}{z}+(1-2z)\deriv{\phi}{z}-\tfrac{1}{4}\phi = 0}
z(1-z)\deriv[2]{\phi}{z}+(1-2z)\deriv{\phi}{z}-\tfrac{1}{4}\phi = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
z*(1 - z)*diff(phi, [z$(2)])+(1 - 2*z)*diff(phi, z)-(1)/(4)*phi = 0

z*(1 - z)*D[\[Phi], {z, 2}]+(1 - 2*z)*D[\[Phi], z]-Divide[1,4]*\[Phi] == 0
Failure Failure
Failed [70 / 70]
Result: -.2165063510-.1250000000*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: -.2165063510-.1250000000*I
Test Values: {phi = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [70 / 70]
Result: Complex[-0.21650635094610968, -0.12499999999999999]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.12499999999999994, -0.21650635094610968]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϕ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
32.10.E34 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;0,0,0,\tfrac{1}{2}) = \Lambda(C_{1}\phi_{1}+C_{2}\phi_{2},z)}
w(z;0,0,0,\tfrac{1}{2}) = \Lambda(C_{1}\phi_{1}+C_{2}\phi_{2},z)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; 0 , 0 , 0 ,(1)/(2)) = Lambda(C[1]*phi[1]+ C[2]*phi[2], z)
 
w[z ; 0 , 0 , 0 ,Divide[1,2]] == \[CapitalLambda][Subscript[C, 1]*Subscript[\[Phi], 1]+ Subscript[C, 2]*Subscript[\[Phi], 2], z]
 Skipped - no semantic math Skipped - no semantic math - -
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