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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 one direct function and elementary functions with respect to a > Involving power function





http://functions.wolfram.com/06.20.21.0010.01









  


  










Input Form





Integrate[a^(\[Alpha] - 1) Beta[Subscript[z, 1], Subscript[z, 2], a, b], a] == (a^(-1 + \[Alpha]) (Subscript[z, 2]^a - Subscript[z, 1]^a))/ (\[Alpha] - 1) + (a^\[Alpha]/(\[Alpha] - 1)) ((Log[Subscript[z, 1]] Gamma[\[Alpha], 0, (-a) Log[Subscript[z, 1]]])/ ((-a) Log[Subscript[z, 1]])^\[Alpha] - (Log[Subscript[z, 2]] Gamma[\[Alpha], 0, (-a) Log[Subscript[z, 2]]])/ ((-a) Log[Subscript[z, 2]])^\[Alpha]) + ((1 - b)/\[Alpha]) a^\[Alpha] Sum[((Pochhammer[2 - b, k] (Subscript[z, 2]^(k + a + 1) - Subscript[z, 1]^(k + a + 1)))/((1 + k)^2 k!)) Hypergeometric2F1[\[Alpha], 1, 1 + \[Alpha], -(a/(1 + k))], {k, 0, Infinity}] /; 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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</annotation> </semantics> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> &#8713; </mo> <mi> &#8469; </mi> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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