Whittaker hypergeometric function M: Series representations (formula 07.44.06.0021)

WhittakerM

$Mathematica Notation$

Hypergeometric Functions

WhittakerM[nu,mu,z]

Series representations

Asymptotic series expansions

http://functions.wolfram.com/07.44.06.0021.01

Input Form

WhittakerM[\[Nu], \[Mu], z] \[Proportional] Gamma[1 + 2 \[Mu]] (((((-z)^(-(1/2) - \[Mu] + \[Nu]) z^(1/2 + \[Mu]))/ Gamma[1/2 + \[Mu] + \[Nu]]) HypergeometricPFQ[{1/2 - \[Mu] - \[Nu], 1/2 + \[Mu] - \[Nu]}, {}, -(1/z)])/E^(z/2) + (1/(z^\[Nu] Gamma[1/2 + \[Mu] - \[Nu]])) E^(z/2) HypergeometricPFQ[{1/2 - \[Mu] + \[Nu], 1/2 + \[Mu] + \[Nu]}, {}, 1/z]) /; (Abs[z] -> Infinity)

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02