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variants of this functions
Beta






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Series representations > Residue representations





http://functions.wolfram.com/06.19.06.0073.01









  


  










Input Form





Beta[z, a, 1 - a + n] == (-(z^a/Gamma[a - n])) (Sum[Residue[(Gamma[s]/((-z)^s (a - s))) Gamma[a - n - s], {s, a - n + j}], {j, 0, n - 1}] + Sum[Residue[(Gamma[s]/((-z)^s (a - s))) Gamma[a - n - s], {s, a - n + j}], {j, n + 1, Infinity}] + Residue[(Gamma[s] (Gamma[a - n - s]/(a - s)))/(-z)^s, {s, a}]) /; Abs[z] > 1 && Element[n, Integers] && n >= 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