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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2},{b1,b2},z] > Differential equations > Ordinary linear differential equations and wronskians > For the direct function itself





http://functions.wolfram.com/07.25.13.0011.01









  


  








Input Form





z^3 Derivative[3][w][z] + (3 - 3 s - r (2 + a z^r) + r (Subscript[b, 1] + Subscript[b, 2])) z^2 Derivative[2][w][z] + (1 + r^2 + 3 (-1 + s) s + r (-1 + 2 s) (2 + a z^r) - a r^2 z^r Subscript[a, 1] - r (a r z^r Subscript[a, 2] + (-1 + r + 2 s) Subscript[b, 2] + Subscript[b, 1] (-1 + r + 2 s - r Subscript[b, 2]))) z Derivative[1][w][z] + ((-a) r z^r (-s + r Subscript[a, 1]) (-s + r Subscript[a, 2]) - s (r + s - r Subscript[b, 1]) (r + s - r Subscript[b, 2])) w[z] == 0 /; w[z] == Subscript[c, 1] z^s HypergeometricPFQRegularized[ {Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2]}, a z^r] + Subscript[c, 2] z^s (MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2]}}, a z^r] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1]}}, a z^r]) + Subscript[c, 3] z^s MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {}}, (-a) z^r]








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