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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/07.33.20.0004.01









  


  










Input Form





Derivative[0, 1, 0][HypergeometricU][a, b, z] == ((Gamma[1 - b] (PolyGamma[1 + a - b] - PolyGamma[1 - b]))/Gamma[1 + a - b]) Hypergeometric1F1[a, b, z] - ((z^(1 - b) Gamma[-1 + b])/Gamma[a]) (Log[z] - PolyGamma[b - 1]) Hypergeometric1F1[1 + a - b, 2 - b, z] + ((a z Gamma[-b])/(b Gamma[1 + a - b])) HypergeometricPFQ[ {{1 + a}, {1}, {1, b}}, {{2, 1 + b}, {}, {1 + b}}, z, z] + ((z^(2 - b) Gamma[b - 1])/((b - 2)^2 Gamma[a])) ((1 + a - b) HypergeometricPFQ[{{2 + a - b}, {1}, {1, 2 - b}}, {{2, 3 - b}, {}, {3 - b}}, z, z] + (b - 2) HypergeometricPFQ[{{2 + a - b}, {1}, {1, 1 + a - b}}, {{2, 3 - b}, {}, {2 + a - b}}, z, 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





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