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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 z==infinity





http://functions.wolfram.com/06.21.06.0055.01









  


  










Input Form





BetaRegularized[z, a, b] \[Proportional] Piecewise[{{(z^a (-z)^(b - 1))/((a + b - 1) Beta[a, b]) - ((Sin[a Pi]/Pi) z^a (Log[-z] - PolyGamma[a] + PolyGamma[a + b]))/ (-z)^a, Element[a + b - 1, Integers] && a + b - 1 > 0}, {((Sin[Pi a]/Pi) z^a (Log[-z] - PolyGamma[a] - EulerGamma))/(-z)^a - (a Sin[Pi a] z^(a - 1))/((-z)^a Pi), a + b == 1}, {(-((-a)!/((-a - b)! (b - 1)!))) (z^(a + b - 1)/(a + b - 1)), Element[-a, Integers] && -a > 0 && Element[b, Integers] && b > 0 && a + b <= 0}, {1, Element[-a, Integers] && -a > 0 && Element[b, Integers] && b > 0 && a + b > 0}}, (Csc[Pi (a + b)] Sin[b Pi] z^a)/(-z)^a + (z^a (-z)^(b - 1))/ ((a + b - 1) Beta[a, b])] /; (Abs[z] -> Infinity)










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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