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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=n+1/2, b=m+1/2





http://functions.wolfram.com/07.33.03.0066.01









  


  








Input Form





HypergeometricU[n + 1/2, m + 1/2, z] == (-1)^(m + n) Gamma[1/2 - n] E^z LaguerreL[-m + n, -(1/2) + m, -z] + (((-1)^(-1 + m) 2^(2 n) m! z^(1/2 - m))/(2 n)!) ((Sqrt[Pi]/Sqrt[z]) E^z Erf[Sqrt[z]] Sum[((k + n)!/k!) LaguerreL[-k + m, 1/2 + k - m, z] LaguerreL[k + n, -(1/2) - k, -z], {k, 0, m}] + Sum[((k + n)!/k!) LaguerreL[-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, 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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Date Added to functions.wolfram.com (modification date)





2007-05-02