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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/07.20.03.0136.01









  


  








Input Form





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