Confluent Hypergeometric Functions - 13.20 Uniform Asymptotic Approximations for Large

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
13.20.E10	${\displaystyle{\displaystyle\zeta=+\sqrt{\frac{x}{\mu}-2-2\ln\left(\frac{x}{2\mu}\right)}}}$ \zeta = +\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}}		zeta = +sqrt((x)/(mu)- 2 - 2*ln((x)/(2*mu)))	\[Zeta] == +Sqrt[Divide[x,\[Mu]]- 2 - 2*Log[Divide[x,2*\[Mu]]]]	Failure	Failure	Failed [300 / 300] Result: .5521389640+.265842778e-1*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 3/2, zeta = 1/2*3^(1/2)+1/2*I} Result: -.8138864400+.3926096818*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 3/2, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[0.552138964202831, 0.026584277433671977] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[0.016922323883714174, -1.2016497569691986] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data
13.20.E10	${\displaystyle{\displaystyle\zeta=-\sqrt{\frac{x}{\mu}-2-2\ln\left(\frac{x}{2\mu}\right)}}}$ \zeta = -\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}}		zeta = -sqrt((x)/(mu)- 2 - 2*ln((x)/(2*mu)))	\[Zeta] == -Sqrt[Divide[x,\[Mu]]- 2 - 2*Log[Divide[x,2*\[Mu]]]]	Failure	Failure	Failed [300 / 300] Result: 1.179911844+.9734157222*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 3/2, zeta = 1/2*3^(1/2)+1/2*I} Result: -.1861135600+1.339441126*I Test Values: {mu = 1/2*3^(1/2)+1/2*I, x = 3/2, zeta = -1/2+1/2*I*3^(1/2)} ... skip entries to safe data	Failed [300 / 300] Result: Complex[1.1799118433660465, 0.9734157225663279] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} Result: Complex[1.7151284836851632, 2.2016497569691986] Test Values: {Rule[x, 1.5], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[μ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} ... skip entries to safe data