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HypergeometricU




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.33.20.0003.01









  


  








Input Form





Derivative[0, 1, 0][HypergeometricU][a, b, z] == (PolyGamma[1 + a - b] - Pi Cot[b Pi]) HypergeometricU[a, b, z] - ((z^(1 - b) Gamma[b - 1] Log[z])/Gamma[a]) Hypergeometric1F1[1 + a - b, 2 - b, z] - (Gamma[1 - b]/Gamma[1 + a - b]) Sum[(PolyGamma[b + k] Pochhammer[a, k] z^k)/(Pochhammer[b, k] k!), {k, 0, Infinity}] - ((z^(1 - b) Gamma[b - 1])/Gamma[a]) Sum[(Pochhammer[1 + a - b, k]/(Pochhammer[2 - b, k] k!)) (PolyGamma[1 + a - b + k] - PolyGamma[2 - b + k]) z^k, {k, 0, Infinity}] /; !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