Legendre and Related Functions - 14.21 Definitions and Basic Properties

From testwiki
Jump to navigation Jump to search


DLMF Formula Constraints Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
14.21.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(1-z^{2}\right)\deriv[2]{w}{z}-2z\deriv{w}{z}+\left(\nu(\nu+1)-\frac{\mu^{2}}{1-z^{2}}\right)w = 0}
\left(1-z^{2}\right)\deriv[2]{w}{z}-2z\deriv{w}{z}+\left(\nu(\nu+1)-\frac{\mu^{2}}{1-z^{2}}\right)w = 0
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(1 - (z)^(2))*diff(w, [z$(2)])- 2*z*diff(w, z)+(nu*(nu + 1)-((mu)^(2))/(1 - (z)^(2)))*w = 0
(1 - (z)^(2))*D[w, {z, 2}]- 2*z*D[w, z]+(\[Nu]*(\[Nu]+ 1)-Divide[\[Mu]^(2),1 - (z)^(2)])*w == 0
Failure Failure
Failed [300 / 300]
Result: 1.366025404+1.366025404*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}

Result: .2113248651+1.366025405*I
Test Values: {mu = 1/2*3^(1/2)+1/2*I, nu = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[1.3660254037844388, 1.3660254037844386]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

Result: Complex[-2.7755575615628914*^-16, -0.9999999999999997]
Test Values: {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data