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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 a > Involving power function





http://functions.wolfram.com/06.19.21.0010.01









  


  








Input Form





Integrate[a^(\[Alpha] - 1) Beta[z, a, b], a] == (z^a a^(-1 + \[Alpha]))/(\[Alpha] - 1) - ((a^\[Alpha]/(\[Alpha] - 1)) Log[z] Gamma[\[Alpha], 0, (-a) Log[z]])/ ((-a) Log[z])^\[Alpha] + ((1 - b)/\[Alpha]) z^(a + 1) a^\[Alpha] Sum[((Pochhammer[2 - b, k] z^k)/((1 + k)^2 k!)) Hypergeometric2F1[\[Alpha], 1, 1 + \[Alpha], -(a/(1 + k))], {k, 0, Infinity}] /; 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