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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/07.33.06.0009.01









  


  










Input Form





HypergeometricU[a, -n, z] == ((-1)^n/Gamma[a]) (((Log[z] z^(n + 1))/(n + 1)!) Hypergeometric1F1[a + n + 1, n + 2, z] - (1/Pochhammer[a, n + 1]) Sum[((-1)^(k + n - 1) Pochhammer[a, k] (n - k)! z^k)/k!, {k, 0, n}] + Sum[(Pochhammer[a + n + 1, k]/((n + k + 1)! k!)) (PolyGamma[a + n + k + 1] - PolyGamma[1 + k] - PolyGamma[n + k + 2]) z^(k + n + 1), {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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2001-10-29





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