Whittaker hypergeometric function M: Representations through more general functions (formula 07.44.26.0074)

WhittakerM

$Mathematica Notation$

Hypergeometric Functions

WhittakerM[nu,mu,z]

Representations through more general functions

Through Meijer G

Generalized cases involving exp and ₁F^~₁

http://functions.wolfram.com/07.44.26.0074.01

Input Form

E^(z/2) Hypergeometric1F1Regularized[c, 2 c, -z] WhittakerM[0, \[Mu], z] == ((2^(1/2 - c + \[Mu]) z^(1/2 + \[Mu]) Gamma[1 + \[Mu]])/Gamma[c]) MeijerG[{{1 + (1/2) (-(1/2) - c - \[Mu]), (1/2) (1/2 - c - \[Mu])}, {}}, {{0}, {1/2 - c - \[Mu], 1/2 - c, -\[Mu]}}, (I z)/2, 1/2]

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