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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/06.21.06.0016.02









  


  








Input Form





BetaRegularized[z, a, 1 - a + n] == ((z^a (-z)^(n - a))/Beta[a, 1 - a + n]) Sum[Pochhammer[a - n, k]/((n - k) k!)/z^k, {k, 0, n - 1}] - (((a Sin[a Pi])/(Pi (n + 1))) z^(a - 1) HypergeometricPFQ[{1, 1, a + 1}, {2, n + 2}, 1/z])/(-z)^a + ((Sin[a Pi]/Pi) z^a (Log[-z] - PolyGamma[a] + PolyGamma[n + 1]))/(-z)^a /; Element[n, Integers] && n >= 0 && !IntervalMemberQ[Interval[{0, 1}], z]








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)





2001-10-29