Painlevé Transcendents - 33.2 Definitions and Basic Properties

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
33.2.E1	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{\rho}+\left(1-\frac{2\eta}{\rho}-\frac{\ell(\ell+1)}{\rho^{2}}\right)w = 0} \deriv[2]{w}{\rho}+\left(1-\frac{2\eta}{\rho}-\frac{\ell(\ell+1)}{\rho^{2}}\right)w = 0	Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }	diff(w, [rho$(2)])+(1 -(2*eta)/(rho)-(ell*(ell + 1))/((rho)^(2)))*w = 0	D[w, {\[Rho], 2}]+(1 -Divide[2*\[Eta],\[Rho]]-Divide[\[ScriptL]*(\[ScriptL]+ 1),\[Rho]^(2)])*w == 0	Failure	Failure	Failed [300 / 300] Result: -11.25833025+5.499999998*I Test Values: {eta = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, ell = 3} Result: -5.499999998-11.25833025*I Test Values: {eta = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, w = -1/2+1/2*I*3^(1/2), ell = 3} ... skip entries to safe data	Failed [294 / 300] Result: Complex[-11.258330249197703, 5.5] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 3], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[10.2583302491977, -3.767949192431125] Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 3], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data