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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 on branch cuts > For the function itself > In the left half-plane





http://functions.wolfram.com/06.21.06.0029.01









  


  










Input Form





BetaRegularized[z, a, b] == (1/Gamma[a]) (1/x)^(a Floor[Arg[z - x]/(2 Pi)]) x^(a (1 + Floor[Arg[z - x]/(2 Pi)])) Sum[(((-1)^k Pochhammer[-a, k - j] x^(j - k))/(j! (k - j)!)) (Gamma[a + j] x^(-a - j) - Gamma[a + b] (1 - x)^(b - j) Hypergeometric2F1Regularized[1, a + b, 1 + b - j, 1 - x]) (z - x)^k, {k, 0, Infinity}, {j, 0, k}] /; Element[x, Reals] && x < 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





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