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HypergeometricU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Differentiation > Low-order differentiation > With respect to a





http://functions.wolfram.com/07.33.20.0001.01









  


  










Input Form





Derivative[1, 0, 0][HypergeometricU][a, b, z] == (Gamma[1 - b]/Gamma[a - b + 1]) Sum[(PolyGamma[a + k] Pochhammer[a, k] z^k)/ (Pochhammer[b, k] k!), {k, 0, Infinity}] + (Gamma[b - 1]/Gamma[a]) z^(1 - b) Sum[(PolyGamma[1 + a - b + k] Pochhammer[1 + a - b, k] z^k)/ (Pochhammer[2 - b, k] k!), {k, 0, Infinity}] - (PolyGamma[a] + PolyGamma[1 + a - b]) HypergeometricU[a, b, z] /; !Element[b, Integers]










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