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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = +\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}}}
\zeta = +\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = -\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}}}
\zeta = -\sqrt{\frac{x}{\mu}-2-2\ln@{\frac{x}{2\mu}}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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 |