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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Series representations > Generalized power series > Expansions at z==0 > Logarithmic case





http://functions.wolfram.com/07.33.06.0007.01









  


  








Input Form





HypergeometricU[a, n, z] == ((-1)^n/Gamma[1 + a - n]) ((Log[z]/(n - 1)!) Hypergeometric1F1[a, n, z] - Sum[(k - 1)!/(z^k (Pochhammer[1 - a, k] (n - k - 1)!)), {k, 1, n - 1}] + Sum[(Pochhammer[a, k]/((n + k - 1)! k!)) (PolyGamma[a + k] - PolyGamma[1 + k] - PolyGamma[n + k]) z^k, {k, 0, Infinity}]) /; Element[n, Integers] && n > 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)





2001-10-29