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WhittakerM




Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerM[nu,mu,z] > Specific values > Specialized values > For fixed mu, z





http://functions.wolfram.com/07.44.03.0017.01









  


  








Input Form





WhittakerM[-(n/2), \[Mu], z] == 2^(-2 + n + 2 \[Mu]) z^((1 - n)/2) (4 BesselI[n/2 + \[Mu], z/2] Gamma[1 + n/2 + \[Mu]] Sum[((-1)^(-j - k + n) z^(2 j - k + n) (-j + k)! Pochhammer[-n, -k + n] Pochhammer[-n + 2 \[Mu], -k + n])/2^(2 (2 j - k + n))/ (j! (-2 j + k)! (-k + n)! Pochhammer[-(n/2) - \[Mu], j] Pochhammer[-(n/2) + \[Mu], -k + n] Pochhammer[1 - k + n/2 + \[Mu], j] Pochhammer[1 + 2 \[Mu], -k + n]), {k, 0, n}, {j, 0, Floor[k/2]}] + z BesselI[1 + n/2 + \[Mu], z/2] Gamma[n/2 + \[Mu]] Sum[((-1)^(-j - k + n) z^(2 j - k + n) (-1 - j + k)! Pochhammer[-n, -k + n] Pochhammer[-n + 2 \[Mu], -k + n])/ 2^(2 (2 j - k + n))/(j! (-1 - 2 j + k)! (-k + n)! Pochhammer[1 - n/2 - \[Mu], j] Pochhammer[-(n/2) + \[Mu], -k + n] Pochhammer[1 - k + n/2 + \[Mu], j] Pochhammer[1 + 2 \[Mu], -k + n]), {k, 0, n}, {j, 0, Floor[(1/2) (-1 + k)]}]) /; Element[n, Integers] && n >= 0








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