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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Representations through more general functions > Through hypergeometric functions > Involving pFq





http://functions.wolfram.com/07.33.26.0003.01









  


  








Input Form





HypergeometricU[a, b, -z] HypergeometricU[a, b, z] == ((Pi (b - 2 a) z^(2 - b/2))/((-z)^(b/2) (b (b - 2) Gamma[a] Gamma[1 + a - b]))) Csc[(b Pi)/2] HypergeometricPFQ[ {1 + a - b/2, 1 - a + b/2}, {3/2, 2 - b/2, 1 + b/2}, z^2/4] - ((Pi z^((3 - b)/2))/((-z)^((b + 1)/2) ((b - 1) Gamma[a] Gamma[1 + a - b]))) Sec[(b Pi)/2] HypergeometricPFQ[{(1 - b)/2 + a, (1 + b)/2 - a}, {1/2, (3 - b)/2, (1 + b)/2}, z^2/4] - ((z^(2 - b) Gamma[b - 1]^2)/((-z)^b Gamma[a]^2)) HypergeometricPFQ[{1 - a, 1 + a - b}, {2 - b, 1 - b/2, (3 - b)/2}, z^2/4] + (Gamma[1 - b]^2/Gamma[1 + a - b]^2) HypergeometricPFQ[{a, -a + b}, {(1 + b)/2, b/2, b}, z^2/4]








Standard Form





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MathML Form







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type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <ci> a </ci> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </list> <list> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29