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





http://functions.wolfram.com/07.33.03.0074.01









  


  








Input Form





HypergeometricU[1/2 - n, m + 1/2, z] == (-(((-z)^(1/2 - m) Gamma[3/2 - m])/Gamma[1 - m - n])) Sum[((-1)^k/k!) (Gamma[-(1/2) + k + m] - Gamma[-(1/2) + k + m, -z]) LaguerreL[-1 - k + m + n, k, z], {k, 0, -1 + m + n}] - (-1)^(m + n) z^(1/2 - m) Gamma[m + n] LaguerreL[-1 + m + n, 1/2 - m, z] /; 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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Date Added to functions.wolfram.com (modification date)





2007-05-02