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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1},{b1,b2},z] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/07.22.16.0001.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1]}, {Subscript[b, 1], Subscript[b, 2]}, c z] HypergeometricPFQ[{Subscript[\[Alpha], 1]}, {Subscript[\[Beta], 1], Subscript[\[Beta], 2]}, d z] == Sum[Subscript[c, k] z^k, {k, 0, Infinity}] /; Subscript[c, k] == ((d^k Pochhammer[Subscript[\[Alpha], 1], k])/ (k! Pochhammer[Subscript[\[Beta], 1], k] Pochhammer[Subscript[\[Beta], 2], k])) HypergeometricPFQ[ {-k, 1 - Subscript[\[Beta], 1] - k, 1 - Subscript[\[Beta], 2] - k, Subscript[a, 1]}, {1 - Subscript[\[Alpha], 1] - k, Subscript[b, 1], Subscript[b, 2]}, c/d] || Subscript[c, k] == ((c^k Pochhammer[Subscript[a, 1], k])/(k! Pochhammer[Subscript[b, 1], k] Pochhammer[Subscript[b, 2], k])) HypergeometricPFQ[ {-k, 1 - Subscript[b, 1] - k, 1 - Subscript[b, 2] - k, Subscript[\[Alpha], 1]}, {1 - Subscript[a, 1] - k, Subscript[\[Beta], 1], Subscript[\[Beta], 2]}, d/c]










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <ci> Subscript </ci> <ci> &#946; </ci> <cn type='integer'> 2 </cn> </apply> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#946; </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#946; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> &#945; </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </list> <apply> <times /> <ci> c </ci> <apply> <power /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <ci> c </ci> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <ci> k </ci> </apply> <apply> <power /> <apply> <times /> <apply> <factorial /> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> k </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> k </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> &#945; </ci> <cn type='integer'> 1 </cn> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <ci> Subscript </ci> <ci> &#946; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#946; </ci> <cn type='integer'> 2 </cn> </apply> </list> <apply> <times /> <ci> d </ci> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29