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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/07.33.03.0064.01









  


  








Input Form





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








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