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variants of this functions
HypergeometricPFQRegularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Integral representations > Contour integral representations





http://functions.wolfram.com/07.32.07.0004.01









  


  










Input Form





HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == (1/(2 Pi I)) (1/Product[Gamma[Subscript[a, k]], {k, 1, p}]) Integrate[(Gamma[s] Product[Gamma[Subscript[a, k] - s], {k, 1, p}])/ Product[Gamma[Subscript[b, k] - s], {k, 1, q}]/(-z)^s, {s, \[Gamma] - I Infinity, \[Gamma] + I Infinity}] /; 0 < \[Gamma] < Min[Re[Subscript[a, 1]], \[Ellipsis], Re[Subscript[a, p]]] && ((p == q + 1 && Abs[Arg[-z]] < Pi) || (p == q && Abs[Arg[-z]] < Pi/2) || (p == q - 1 && \[Gamma] < 1/4 + (1/2) Re[Sum[Subscript[b, j], {j, 1, q}] - Sum[Subscript[a, j], {j, 1, p}]]))










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





© 1998- Wolfram Research, Inc.