Confluent Hypergeometric Functions - 13.25 Products

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.25.E1	${\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)M_{\kappa,-\mu-1}\left(z\right)+\frac{(\frac{1}{2}+\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+\mu)(1+2\mu)^{2}}M_{\kappa,\mu+1}\left(z\right)M_{\kappa,-\mu}\left(z\right)=1}}$ \WhittakerconfhyperM{\kappa}{\mu}@{z}\WhittakerconfhyperM{\kappa}{-\mu-1}@{z}+\frac{(\frac{1}{2}+\mu+\kappa)(\frac{1}{2}+\mu-\kappa)}{4\mu(1+\mu)(1+2\mu)^{2}}\WhittakerconfhyperM{\kappa}{\mu+1}@{z}\WhittakerconfhyperM{\kappa}{-\mu}@{z} = 1		WhittakerM(kappa, mu, z)*WhittakerM(kappa, - mu - 1, z)+(((1)/(2)+ mu + kappa)*((1)/(2)+ mu - kappa))/(4*mu*(1 + mu)*(1 + 2*mu)^(2))*WhittakerM(kappa, mu + 1, z)*WhittakerM(kappa, - mu, z) = 1	WhittakerM[\[Kappa], \[Mu], z]*WhittakerM[\[Kappa], - \[Mu]- 1, z]+Divide[(Divide[1,2]+ \[Mu]+ \[Kappa])*(Divide[1,2]+ \[Mu]- \[Kappa]),4*\[Mu]*(1 + \[Mu])*(1 + 2*\[Mu])^(2)]*WhittakerM[\[Kappa], \[Mu]+ 1, z]*WhittakerM[\[Kappa], - \[Mu], z] == 1	Failure	Failure	Failed [168 / 300] Result: Float(infinity)+Float(infinity)*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = -3/2, z = 1/2*3^(1/2)+1/2*I} Result: Float(infinity)+Float(infinity)*I Test Values: {kappa = 1/2*3^(1/2)+1/2*I, mu = -3/2, z = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [162 / 300] Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, -1.5]} Result: Indeterminate Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, 1.5]} ... skip entries to safe data