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variants of this functions
Hypergeometric1F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1[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=1/2+-m





http://functions.wolfram.com/07.20.03.0139.01









  


  








Input Form





Hypergeometric1F1[1/2 - n, 1/2 + m, z] == (((-1)^(-1 + m) Sqrt[Pi])/2) z^(1/2 - m) Erfi[Sqrt[z]] Pochhammer[3/2, -1 + m] Sum[Binomial[n, k] LaguerreL[-1 + k + m, 1/2 - k - m, z], {k, 0, n}] + (1/2) (-1)^(-1 + m) E^z z^(1 - m) Pochhammer[3/2, -1 + m] Sum[Binomial[n, k] Sum[(1/p) LaguerreL[-1 + k + m - p, 1/2 - k - m + p, z] LaguerreL[-1 + p, 1/2 - p, -z], {p, 1, -1 + k + m}], {k, 0, n}] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0








Standard 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