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variants of this functions
Beta






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Integration > Indefinite integration > Involving one direct function and elementary functions with respect to b > Involving power function





http://functions.wolfram.com/06.19.21.0012.01









  


  










Input Form





Integrate[b^(\[Alpha] - 1) Beta[z, a, b], b] == Sum[(((-1)^k k! z^(j + a) b^(k + \[Alpha]))/((a + j) (k + \[Alpha]) k! j!)) StirlingS1[j, k] HypergeometricPFQ[{1 + j, a + j}, {1 + a + j}, z], {j, 0, Infinity}, {k, 0, j}] /; Abs[z] < 1 && !(Element[-a, Integers] && -a >= 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)





2001-10-29





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