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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Series representations > Generalized power series > Expansions at generic point b==b0 > For the function itself





http://functions.wolfram.com/06.19.06.0069.01









  


  








Input Form





Beta[z, a, b] \[Proportional] Beta[z, a, Subscript[b, 0]] + ((1 - z)^Subscript[b, 0] Gamma[Subscript[b, 0]]^2 HypergeometricPFQRegularized[{1 - a, Subscript[b, 0], Subscript[b, 0]}, {1 + Subscript[b, 0], 1 + Subscript[b, 0]}, 1 - z] - Beta[1 - z, Subscript[b, 0], a] Log[1 - z] + Beta[a, Subscript[b, 0]] (PolyGamma[Subscript[b, 0]] - PolyGamma[a + Subscript[b, 0]])) (b - Subscript[b, 0]) + (1/2) (((2 (1 - z)^Subscript[b, 0])/Subscript[b, 0]^3) (-HypergeometricPFQ[{1 - a, Subscript[b, 0], Subscript[b, 0], Subscript[b, 0]}, {1 + Subscript[b, 0], 1 + Subscript[b, 0], 1 + Subscript[b, 0]}, 1 - z] + Subscript[b, 0] Log[1 - z] HypergeometricPFQ[{1 - a, Subscript[b, 0], Subscript[b, 0]}, {1 + Subscript[b, 0], 1 + Subscript[b, 0]}, 1 - z]) + Beta[a, Subscript[b, 0]] ((PolyGamma[Subscript[b, 0]] - PolyGamma[a + Subscript[b, 0]])^2 + PolyGamma[1, Subscript[b, 0]] - PolyGamma[1, a + Subscript[b, 0]]) - Beta[1 - z, Subscript[b, 0], a] Log[1 - z]^2) (b - Subscript[b, 0])^2 + \[Ellipsis] /; (b -> Subscript[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)





2007-05-02