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variants of this functions
HypergeometricPFQRegularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Integration > Definite integration > For the direct function itself





http://functions.wolfram.com/07.32.21.0003.01









  


  








Input Form





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








Standard Form





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MathML Form







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</ms> <apply> <ci> RowBox </ci> <list> <ms> min </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> Re </ms> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> 1 </ms> </apply> <ms> ) </ms> </list> </apply> <ms> , </ms> <ms> &#8230; </ms> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <ms> Re </ms> <ms> ( </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> p </ms> </apply> <ms> ) </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <ms> 4 </ms> </apply> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <ms> 2 </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> Re </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> &#8721; </ms> <apply> <ci> RowBox </ci> <list> <ms> j </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> p </ms> </apply> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> j </ms> </apply> </list> </apply> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> &#8721; </ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> q </ms> </apply> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> k </ms> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> &#8743; </ms> <apply> <ci> RowBox </ci> <list> <ms> q </ms> <ms> &#10869; </ms> <apply> <ci> RowBox </ci> <list> <ms> p </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29