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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 unit





http://functions.wolfram.com/07.27.13.0015.01









  


  










Input Form





(1 - z) z^2 Derivative[3][w][z] + (Subscript[b, 1] + Subscript[b, 2] + 1 - (Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + 3) z) z Derivative[2][w][z] + (Subscript[b, 1] Subscript[b, 2] - (Subscript[a, 1] Subscript[a, 2] + Subscript[a, 2] Subscript[a, 3] + Subscript[a, 1] Subscript[a, 3] + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + 1) z) Derivative[1][w][z] - Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] w[z] == 0 /; w[z] == Subscript[c, 1] MeijerG[{{}, {1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {}}, z] + Subscript[c, 2] MeijerG[{{0, Subscript[b, 1], 1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, Subscript[b, 1]}, {0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}}, z] + Subscript[c, 3] MeijerG[{{0, Subscript[b, 2], 1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, Subscript[b, 2]}, {0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}}, z] && Abs[z] < 1 && !Element[Subscript[b, 1] + Subscript[b, 2] - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3], Integers] && !Element[Subscript[b, 1], Integers] && !Element[Subscript[b, 2], Integers] && !Element[Subscript[b, 1] - Subscript[b, 2], Integers]










Standard Form





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MathML Form







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





2007-05-02