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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=n, b=1/2+-m





http://functions.wolfram.com/07.20.03.0123.01









  


  








Input Form





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








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