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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/06.21.06.0026.01









  


  










Input Form





BetaRegularized[z, a, b] \[Proportional] (Sin[Pi b]/(Pi Gamma[a])) (1/x)^(a Floor[Arg[z - x]/(2 Pi)]) x^(a (1 + Floor[Arg[z - x]/(2 Pi)])) (MeijerG[{{1 - a, b}, {}}, {{0, b}, {}}, 1 - x] + (1/x) (a MeijerG[{{1 - a, b}, {}}, {{0, b}, {}}, 1 - x] + x MeijerG[{{-a, -1 + b}, {}}, {{0, -1 + b}, {}}, 1 - x]) (z - x) + (1/(2 x^2)) (x^2 MeijerG[{{-1 - a, -2 + b}, {}}, {{0, -2 + b}, {}}, 1 - x] + a ((-1 + a) MeijerG[{{1 - a, b}, {}}, {{0, b}, {}}, 1 - x] + 2 x MeijerG[{{-a, -1 + b}, {}}, {{0, -1 + b}, {}}, 1 - x])) (z - x)^2 + \[Ellipsis]) /; (z -> x) && 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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