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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z1,z2,a,b] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/06.20.26.0006.01









  


  








Input Form





Beta[Subscript[z, 1], Subscript[z, 2], a, b] == Beta[1 - a - b, a] (Subscript[z, 2]^a/(-Subscript[z, 2])^a - Subscript[z, 1]^a/(-Subscript[z, 1])^a) + (1/(a + b - 1)) ((-Subscript[z, 2])^(b - 1) Subscript[z, 2]^a HypergeometricPFQ[{1 - b, 1 - a - b}, {2 - a - b}, 1/Subscript[z, 2]] - (-Subscript[z, 1])^(b - 1) Subscript[z, 1]^a HypergeometricPFQ[ {1 - b, 1 - a - b}, {2 - a - b}, 1/Subscript[z, 1]]) /; !(Element[a + b, Integers] && a + b > 0)








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