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variants of this functions
BetaRegularized




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.21.06.0062.01









  


  








Input Form





BetaRegularized[z, a, b] \[Proportional] BetaRegularized[z, a, Subscript[b, 0]] + ((1 - z)^Subscript[b, 0]/Gamma[a]) Gamma[a + Subscript[b, 0]] ((Gamma[Subscript[b, 0]] HypergeometricPFQRegularized[ {1 - a, Subscript[b, 0], Subscript[b, 0]}, {1 + Subscript[b, 0], 1 + Subscript[b, 0]}, 1 - z] - Hypergeometric2F1Regularized[1 - a, Subscript[b, 0], 1 + Subscript[b, 0], 1 - z] (Log[1 - z] - PolyGamma[Subscript[b, 0]] + PolyGamma[a + Subscript[b, 0]])) (b - Subscript[b, 0]) - (Gamma[Subscript[b, 0]]^2 HypergeometricPFQRegularized[ {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] - Gamma[Subscript[b, 0]] (Log[1 - z] - PolyGamma[Subscript[b, 0]] + PolyGamma[a + Subscript[b, 0]]) HypergeometricPFQRegularized[{1 - a, Subscript[b, 0], Subscript[b, 0]}, {1 + Subscript[b, 0], 1 + Subscript[b, 0]}, 1 - z] + (1/2) (Log[1 - z]^2 + (PolyGamma[Subscript[b, 0]] - PolyGamma[a + Subscript[b, 0]]) (-2 Log[1 - z] + PolyGamma[Subscript[b, 0]] - PolyGamma[a + Subscript[b, 0]]) - PolyGamma[1, Subscript[b, 0]] + PolyGamma[1, a + Subscript[b, 0]]) Hypergeometric2F1Regularized[1 - a, Subscript[b, 0], 1 + Subscript[b, 0], 1 - z]) (b - Subscript[b, 0])^2 + O[(b - Subscript[b, 0])^3])








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