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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself > Representation of fundamental system solutions near zero





http://functions.wolfram.com/07.27.13.0012.01









  


  










Input Form





Wronskian[z^s HypergeometricPFQRegularized[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, a z^r], z^s (MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2]}}, a z^r] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1]}}, a z^r]), z^s MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {}}, (-a) z^r], z] == a^3 r^3 z^(-3 + 3 r + 3 s) ((-a) z^r)^(-Subscript[b, 1] - Subscript[b, 2]) (a z^r)^(-1 - Subscript[b, 1] - Subscript[b, 2]) (1 - a z^r)^(-2 - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] + Subscript[b, 1] + Subscript[b, 2]) (((-a) z^r)^Subscript[b, 2] (a z^r)^Subscript[b, 1] + ((-a) z^r)^Subscript[b, 1] (a z^r)^Subscript[b, 2]) Gamma[1 + Subscript[a, 1] - Subscript[b, 1]] Gamma[1 + Subscript[a, 2] - Subscript[b, 1]] Gamma[1 + Subscript[a, 3] - Subscript[b, 1]] Gamma[1 + Subscript[a, 1] - Subscript[b, 2]] Gamma[1 + Subscript[a, 2] - Subscript[b, 2]] Gamma[1 + Subscript[a, 3] - Subscript[b, 2]]










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