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variants of this functions
HypergeometricPFQRegularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Identities > Functional identities > Division on even and odd parts and generalization





http://functions.wolfram.com/07.32.17.0021.01









  


  








Input Form





HypergeometricPFQRegularized[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == SuperPlus[A][z] + SuperMinus[A][z] /; SuperPlus[A][z] == 2^(q - \[Eta]) Pi^((q + 1)/2) HypergeometricPFQRegularized[{Subscript[a, 1]/2, \[Ellipsis], Subscript[a, p]/2, (Subscript[a, 1] + 1)/2, \[Ellipsis], (Subscript[a, p] + 1)/2}, {1/2, Subscript[b, 1]/2, \[Ellipsis], Subscript[b, q]/2, (Subscript[b, 1] + 1)/2, \[Ellipsis], (Subscript[b, q] + 1)/2}, 4^(p - q - 1) z^2] && SuperMinus[A][z] == 2^(-\[Eta] - 1) Pi^((q + 1)/2) Product[Subscript[a, j], {j, 1, p}] z HypergeometricPFQRegularized[ {(Subscript[a, 1] + 1)/2, \[Ellipsis], (Subscript[a, p] + 1)/2, (Subscript[a, 1] + 2)/2, \[Ellipsis], (Subscript[a, p] + 2)/2}, {3/2, (Subscript[b, 1] + 1)/2, \[Ellipsis], (Subscript[b, q] + 1)/2, (Subscript[b, 1] + 2)/2, \[Ellipsis], (Subscript[b, q] + 2)/2}, 4^(p - q - 1) z^2] && \[Eta] == Sum[Subscript[b, j], {j, 1, q}]








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