Whittaker hypergeometric function M: Transformations (formula 07.44.16.0005)

WhittakerM

$Mathematica Notation$

Hypergeometric Functions

WhittakerM[nu,mu,z]

Transformations

Products, sums, and powers of the direct function

Products of the direct function

http://functions.wolfram.com/07.44.16.0005.01

Input Form

WhittakerM[\[Nu], \[Mu], c z] WhittakerM[\[Lambda], \[Gamma], d z] == ((c z)^(1/2 + \[Mu]) (d z)^(1/2 + \[Gamma]) Sum[z^k Subscript[c, k], {k, 0, Infinity}])/E^((1/2) (c + d) z) /; Subscript[c, k] == ((d^k Pochhammer[1/2 + \[Gamma] - \[Lambda], k])/ (k! Pochhammer[1 + 2 \[Gamma], k])) HypergeometricPFQ[ {-k, -k - 2 \[Gamma], 1/2 + \[Mu] - \[Nu]}, {1/2 - k - \[Gamma] + \[Lambda], 1 + 2 \[Mu]}, -(c/d)] || Subscript[c, k] == ((c^k Pochhammer[1/2 + \[Mu] - \[Nu], k])/ (k! Pochhammer[1 + 2 \[Mu], k])) HypergeometricPFQ[ {-k, -k - 2 \[Mu], 1/2 + \[Gamma] - \[Lambda]}, {1/2 - k - \[Mu] + \[Nu], 1 + 2 \[Gamma]}, -(d/c)]

Standard Form

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MathML Form

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type='integer'> 1 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> d </ci> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02