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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z1,z2,a,b] > Integration > Indefinite integration > Involving only one direct function with respect to b





http://functions.wolfram.com/06.20.21.0011.01









  


  








Input Form





Integrate[Beta[Subscript[z, 1], Subscript[z, 2], a, b], b] == Sum[(((-1)^k k! b^(k + 1))/((a + j) (k + 1)! j!)) StirlingS1[j, k] (Subscript[z, 2]^(j + a) HypergeometricPFQ[{1 + j, a + j}, {1 + a + j}, Subscript[z, 2]] - Subscript[z, 1]^(j + a) HypergeometricPFQ[ {1 + j, a + j}, {1 + a + j}, Subscript[z, 1]]), {j, 0, Infinity}, {k, 0, j}] /; Abs[Subscript[z, 1]] < 1 && Abs[Subscript[z, 2]] < 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