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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2},{b1,b2,b3},z] > Integration > Definite integration > For the direct function itself





http://functions.wolfram.com/07.26.21.0003.01









  


  










Input Form





Integrate[t^(\[Alpha] - 1) HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, -t], {t, 0, Infinity}] == (Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[b, 3]] Gamma[\[Alpha]] Gamma[-\[Alpha] + Subscript[a, 1]] Gamma[-\[Alpha] + Subscript[a, 2]])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]] Gamma[-\[Alpha] + Subscript[b, 1]] Gamma[-\[Alpha] + Subscript[b, 2]] Gamma[-\[Alpha] + Subscript[b, 3]]) /; 0 < Re[\[Alpha]] < Min[Re[Subscript[a, 1]], Re[Subscript[a, 2]], 1/4 - (1/2) Re[Sum[Subscript[a, 1], {j, 1, 2}] - Sum[Subscript[b, k], {k, 1, 3}]]]










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