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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/07.20.03.0142.01









  


  








Input Form





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








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