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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2},{b1,b2},z] > Identities > Functional identities > Division on even and odd parts and generalization





http://functions.wolfram.com/07.25.17.0021.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2]}, z] == Sum[(z^k/k!) ((Pochhammer[Subscript[a, 1], k] Pochhammer[Subscript[a, 2], k])/(Pochhammer[Subscript[b, 1], k] Pochhammer[Subscript[b, 2], k])) HypergeometricPFQ[{1, (Subscript[a, 1] + k)/n, \[Ellipsis], (Subscript[a, 1] + k + n - 1)/n, (Subscript[a, 2] + k)/n, \[Ellipsis], (Subscript[a, 2] + k + n - 1)/n}, {(k + 1)/n, \[Ellipsis], (k + n)/n, (Subscript[b, 1] + k)/n, \[Ellipsis], (Subscript[b, 1] + k + n - 1)/n, (Subscript[b, 2] + k)/n, \[Ellipsis], (Subscript[b, 2] + k + n - 1)/n}, z^n/n^n], {k, 0, n - 1}]










Standard Form





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MathML Form







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





2001-10-29





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