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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Specific values > Specialized values > For fixed z and with symbolical integers in parameters > For fixed z and a=1/2+-n, b=-m





http://functions.wolfram.com/07.33.03.0047.01









  


  








Input Form





HypergeometricU[1/2 - n, -m, z] == (1/Sqrt[Pi]) (2^(-1 - m) E^(z/2) z^(1 + m) Sum[(z^k Binomial[-1 - m + n, k] Pochhammer[1/2 - n, -1 - k - m + n] Sum[(Binomial[1 + k + m, p] Sum[BesselK[-2 j + p, z/2] Binomial[p, j], {j, 0, p}])/2^p, {p, 0, 1 + k + m}])/2^k, {k, 0, -1 - m + n}]) /; Element[n, Integers] && n > m && Element[m, Integers] && m >= -1








Standard Form





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MathML Form







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Rule Form





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Contributed by





Brychkov Yu.A. (2006)


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





2007-05-02