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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > Representation of fundamental system solutions near point z=ComplexInfinity for p>=q+1 in the general case





http://functions.wolfram.com/07.31.13.0009.01









  


  










Input Form





D[Fold[Function[{f, k}, z D[f, z] + (Subscript[b, k] - 1) f], w[z], {1, \[Ellipsis], q}], z] - Fold[Function[{f, l}, z D[f, z] + Subscript[a, l] f], w[z], {1, \[Ellipsis], p}] == 0 /; w[z] == Sum[(Subscript[c, k] HypergeometricPFQRegularized[ {Subscript[a, k], 1 + Subscript[a, k] - Subscript[b, 1], \[Ellipsis], 1 + Subscript[a, k] - Subscript[b, q]}, {1 + Subscript[a, k] - Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, k] - Subscript[a, k - 1], 1 + Subscript[a, k] - Subscript[a, k + 1], \[Ellipsis], 1 + Subscript[a, k] - Subscript[a, p]}, (-1)^(1 - p + q)/z])/z^Subscript[a, k], {k, 1, p}] && ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= p && 1 <= k <= p, !Element[Subscript[a, j] - Subscript[a, k], Integers]]










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)





2007-05-02





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