Painlevé Transcendents - 32.9 Other Elementary Solutions

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
32.9.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;\mu,0,0,-\mu\kappa^{3}) = \kappa z^{1/3}}
w(z;\mu,0,0,-\mu\kappa^{3}) = \kappa z^{1/3}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; mu , 0 , 0 , - mu*(kappa)^(3)) = kappa*(z)^(1/3)
 
w[z ; \[Mu], 0 , 0 , - \[Mu]*\[Kappa]^(3)] == \[Kappa]*(z)^(1/3)
 Skipped - no semantic math Skipped - no semantic math - -
32.9.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;0,-2\kappa,0,4\kappa\mu-\lambda^{2}) = z(\kappa(\ln@@{z})^{2}+\lambda\ln@@{z}+\mu)}
w(z;0,-2\kappa,0,4\kappa\mu-\lambda^{2}) = z(\kappa(\ln@@{z})^{2}+\lambda\ln@@{z}+\mu)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; 0 , - 2*kappa(,)*0 , 4*kappa(mu)- (lambda)^(2)) = z*((kappa(ln(z)))^(2)+ lambda*ln(z)+ mu)

w[z ; 0 , - 2*\[Kappa][,]*0 , 4*\[Kappa][Mu]- \[Lambda]^(2)] == z*((\[Kappa][Log[z]])^(2)+ \[Lambda]*Log[z]+ \[Mu])
Translation Error Translation Error - -
32.9.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;-\nu^{2}\lambda,0,\nu^{2}(\lambda^{2}-4\kappa\mu),0) = \dfrac{z^{\nu-1}}{\kappa z^{2\nu}+\lambda z^{\nu}+\mu}}
w(z;-\nu^{2}\lambda,0,\nu^{2}(\lambda^{2}-4\kappa\mu),0) = \dfrac{z^{\nu-1}}{\kappa z^{2\nu}+\lambda z^{\nu}+\mu}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; - (nu)^(2)* lambda , 0 , (nu)^(2)*((lambda)^(2)- 4*kappa*mu), 0) = ((z)^(nu - 1))/(kappa*(z)^(2*nu)+ lambda*(z)^(nu)+ mu)
 
w[z ; - \[Nu]^(2)* \[Lambda], 0 , \[Nu]^(2)*(\[Lambda]^(2)- 4*\[Kappa]*\[Mu]), 0] == Divide[(z)^(\[Nu]- 1),\[Kappa]*(z)^(2*\[Nu])+ \[Lambda]*(z)^\[Nu]+ \[Mu]]
 Skipped - no semantic math Skipped - no semantic math - -
32.9.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = 2n}
\beta = 2n		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta = 2*n
 
\[Beta] == 2*n
 Skipped - no semantic math Skipped - no semantic math - -
32.9.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \ifrac{P_{n^{2}+1}(\zeta)}{Q_{n^{2}}(\zeta)}}
w(z) = \ifrac{P_{n^{2}+1}(\zeta)}{Q_{n^{2}}(\zeta)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z) = (P[(n)^(2)+ 1](zeta))/(Q[(n)^(2)](zeta))
 
w[z] == Divide[Subscript[P, (n)^(2)+ 1][\[Zeta]],Subscript[Q, (n)^(2)][\[Zeta]]]
 Skipped - no semantic math Skipped - no semantic math - -
32.9.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;\mu,-\tfrac{1}{8},-\mu\kappa^{2},0) = 1+\kappa z^{1/2}}
w(z;\mu,-\tfrac{1}{8},-\mu\kappa^{2},0) = 1+\kappa z^{1/2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; mu , -(1)/(8), - mu*(kappa)^(2), 0) = 1 + kappa*(z)^(1/2)
 
w[z ; \[Mu], -Divide[1,8], - \[Mu]*\[Kappa]^(2), 0] == 1 + \[Kappa]*(z)^(1/2)
 Skipped - no semantic math Skipped - no semantic math - -
32.9.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;0,0,\mu,-\tfrac{1}{2}\mu^{2}) = \kappa\exp@{\mu z}}
w(z;0,0,\mu,-\tfrac{1}{2}\mu^{2}) = \kappa\exp@{\mu z}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ; 0 , 0 , mu , -(1)/(2)*(mu)^(2)) = kappa*exp(mu*z)

w[z ; 0 , 0 , \[Mu], -Divide[1,2]*\[Mu]^(2)] == \[Kappa]*Exp[\[Mu]*z]
Translation Error Translation Error - -
32.9.E9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mspace{17.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{2}\mu^{2},-\tfrac{1}{8}(2n-1)^{2},-1)}
\mspace{17.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{2}\mu^{2},-\tfrac{1}{8}(2n-1)^{2},-1)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(alpha , beta , gamma) = ((1)/(2)*(mu)^(2), -(1)/(8)*(2*n - 1)^(2), - 1)
 
(\[Alpha], \[Beta], \[Gamma]) == (Divide[1,2]*\[Mu]^(2), -Divide[1,8]*(2*n - 1)^(2), - 1)
 Skipped - no semantic math Skipped - no semantic math - -
32.9.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mspace{5.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{8}(2n-1)^{2},-\tfrac{1}{2}\mu^{2},1)}
\mspace{5.0mu }(\alpha,\beta,\gamma) = (\tfrac{1}{8}(2n-1)^{2},-\tfrac{1}{2}\mu^{2},1)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
(alpha , beta , gamma) = ((1)/(8)*(2*n - 1)^(2), -(1)/(2)*(mu)^(2), 1)
 
(\[Alpha], \[Beta], \[Gamma]) == (Divide[1,8]*(2*n - 1)^(2), -Divide[1,2]*\[Mu]^(2), 1)
 Skipped - no semantic math Skipped - no semantic math - -
32.9.E11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z) = \ifrac{P_{n^{2}-n+1}(\zeta)}{Q_{n^{2}-n}(\zeta)}}
w(z) = \ifrac{P_{n^{2}-n+1}(\zeta)}{Q_{n^{2}-n}(\zeta)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z) = (P[(n)^(2)- n + 1](zeta))/(Q[(n)^(2)- n](zeta))
 
w[z] == Divide[Subscript[P, (n)^(2)- n + 1][\[Zeta]],Subscript[Q, (n)^(2)- n][\[Zeta]]]
 Skipped - no semantic math Skipped - no semantic math - -
32.9.E13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle w(z;\tfrac{1}{2}\kappa^{2},-\tfrac{1}{2}\kappa^{2},\tfrac{1}{2}\mu^{2},\tfrac{1}{2}(1-\mu^{2})) = z^{1/2}}
w(z;\tfrac{1}{2}\kappa^{2},-\tfrac{1}{2}\kappa^{2},\tfrac{1}{2}\mu^{2},\tfrac{1}{2}(1-\mu^{2})) = z^{1/2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
w(z ;(1)/(2)*(kappa)^(2), -(1)/(2)*(kappa)^(2),(1)/(2)*(mu)^(2),(1)/(2)*(1 - (mu)^(2))) = (z)^(1/2)
 
w[z ;Divide[1,2]*\[Kappa]^(2), -Divide[1,2]*\[Kappa]^(2),Divide[1,2]*\[Mu]^(2),Divide[1,2]*(1 - \[Mu]^(2))] == (z)^(1/2)
 Skipped - no semantic math Skipped - no semantic math - -
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