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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/07.28.16.0001.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, c z] HypergeometricPFQ[{Subscript[\[Alpha], 1], Subscript[\[Alpha], 2], Subscript[\[Alpha], 3], Subscript[\[Alpha], 4]}, {Subscript[\[Beta], 1], Subscript[\[Beta], 2], Subscript[\[Beta], 3]}, d z] == Sum[Subscript[c, k] z^k, {k, 0, Infinity}] /; Subscript[c, k] == ((d^k Product[Pochhammer[Subscript[\[Alpha], j], k], {j, 1, 4}])/(k! Product[Pochhammer[Subscript[\[Beta], j], k], {j, 1, 3}])) HypergeometricPFQ[{-k, 1 - Subscript[\[Beta], 1] - k, 1 - Subscript[\[Beta], 2] - k, 1 - Subscript[\[Beta], 3] - k, Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {1 - Subscript[\[Alpha], 1] - k, 1 - Subscript[\[Alpha], 2] - k, 1 - Subscript[\[Alpha], 3] - k, 1 - Subscript[\[Alpha], 4] - k, Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, c/d] || Subscript[c, k] == ((c^k Product[Pochhammer[Subscript[a, j], k], {j, 1, 4}])/(k! Product[Pochhammer[Subscript[b, j], k], {j, 1, 3}])) HypergeometricPFQ[{-k, 1 - Subscript[b, 1] - k, 1 - Subscript[b, 2] - k, 1 - Subscript[b, 3] - k, Subscript[\[Alpha], 1], Subscript[\[Alpha], 2], Subscript[\[Alpha], 3], Subscript[\[Alpha], 4]}, {1 - Subscript[a, 1] - k, 1 - Subscript[a, 2] - k, 1 - Subscript[a, 3] - k, 1 - Subscript[a, 4] - k, Subscript[\[Beta], 1], Subscript[\[Beta], 2], Subscript[\[Beta], 3]}, d/c]










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





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