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variants of this functions
HypergeometricPFQRegularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Specific values > Specialized values > Case pF~qwith fixed a1, ..., ap





http://functions.wolfram.com/07.32.03.0010.01









  


  










Input Form





HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[a, 1] + Subscript[m, 1], \[Ellipsis], Subscript[a, n] + Subscript[m, n], Subscript[b, n + 1], \[Ellipsis], Subscript[b, q]}, z] == (1/Product[Gamma[Subscript[a, j]] (Subscript[m, j] - 1)!, {j, 1, n}]) Sum[\[Ellipsis] Sum[Gamma[Subscript[a, k] + Subscript[j, k]] Product[(Pochhammer[1 - Subscript[m, l], Subscript[j, l]]/ Subscript[j, l]!) Product[If[i == k, 1, 1/(Subscript[a, i] + Subscript[j, i] - Subscript[a, k] - Subscript[j, k])] HypergeometricPFQRegularized[{Subscript[a, k] + Subscript[j, k], Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}, {Subscript[a, k] + Subscript[j, k] + 1, Subscript[b, n + 1], \[Ellipsis], Subscript[b, q]}, z], {i, 1, n}], {l, 1, n}], {Subscript[j, n], 0, Subscript[m, n] - 1}], {k, 1, n}, {Subscript[j, 1], 0, Subscript[m, 1] - 1}] /; Element[Subscript[m, n], Integers] && Subscript[m, n] > 0 && n <= q










Standard Form





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MathML Form







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</ms> <apply> <ci> RowBox </ci> <list> <ms> k </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> n </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> &#8721; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> 1 </ms> </apply> <ms> = </ms> <ms> 0 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> m </ms> <ms> 1 </ms> </apply> <ms> - </ms> <ms> 1 </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#8230; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> &#8721; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> n </ms> </apply> <ms> = </ms> <ms> 0 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> m </ms> <ms> n </ms> </apply> <ms> - </ms> <ms> 1 </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> &#915; </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> <ms> + </ms> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> k </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> &#8719; </ms> <apply> <ci> RowBox </ci> <list> <ms> l </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <ms> n </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> SubscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> m </ms> <ms> l </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> l </ms> </apply> </apply> <ci> Pochhammer </ci> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> l </ms> </apply> <ms> ! </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> UnderoverscriptBox </ci> <ms> &#8719; </ms> <apply> <ci> UnderscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> i </ms> <ms> = </ms> <ms> 1 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> i </ms> <ms> &#8800; </ms> <ms> k </ms> </list> </apply> </apply> <ms> n </ms> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 1 </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> i </ms> </apply> <ms> + </ms> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> i </ms> </apply> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> <ms> - </ms> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> k </ms> </apply> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> &#62387; </ms> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <ms> p </ms> <ms> - </ms> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ci> TraditionalForm </ci> </apply> </apply> <apply> <ci> SubscriptBox </ci> <apply> <ci> OverscriptBox </ci> <ms> F </ms> <ms> ~ </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> q </ms> <ms> - </ms> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> </list> </apply> <ms> &#8289; </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> <ms> + </ms> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> k </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> <ms> , </ms> <ms> &#8230; </ms> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> p </ms> </apply> </list> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <list> <apply> <ci> SlotSequence </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> </apply> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <list> <apply> <ci> SlotSequence </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> </apply> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> ; </ms> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> TagBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> a </ms> <ms> k </ms> </apply> <ms> + </ms> <apply> <ci> SubscriptBox </ci> <ms> j </ms> <ms> k </ms> </apply> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <apply> <ci> RowBox </ci> <list> <ms> n </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> <ms> , </ms> <ms> &#8230; </ms> <ms> , </ms> <apply> <ci> SubscriptBox </ci> <ms> b </ms> <ms> q </ms> </apply> </list> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <list> <apply> <ci> SlotSequence </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> </apply> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <apply> <ci> InterpretTemplate </ci> <apply> <ci> Function </ci> <list> <apply> <ci> SlotSequence </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> </apply> </apply> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> ; </ms> <apply> <ci> TagBox </ci> <ms> z </ms> <ci> HypergeometricPFQ </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </list> </apply> </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





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