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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},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/07.28.13.0004.01









  


  










Input Form





(1 - z) z^3 Derivative[4][w][z] + (3 + Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] - (6 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4]) z) z^2 Derivative[3][w][z] + (1 + Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 2] Subscript[b, 3] + Subscript[b, 1] Subscript[b, 3] - (7 + 3 Subscript[a, 1] + 3 Subscript[a, 2] + 3 Subscript[a, 3] + 3 Subscript[a, 4] + Subscript[a, 1] Subscript[a, 2] + Subscript[a, 1] Subscript[a, 3] + Subscript[a, 1] Subscript[a, 4] + Subscript[a, 2] Subscript[a, 3] + Subscript[a, 2] Subscript[a, 4] + Subscript[a, 3] Subscript[a, 4]) z) z Derivative[2][w][z] + (Subscript[b, 1] Subscript[b, 2] Subscript[b, 3] - (1 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 1] Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] + Subscript[a, 1] Subscript[a, 3] + Subscript[a, 2] Subscript[a, 3] + Subscript[a, 1] Subscript[a, 4] + Subscript[a, 2] Subscript[a, 4] + Subscript[a, 3] Subscript[a, 4] + Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] + Subscript[a, 1] Subscript[a, 2] Subscript[a, 4] + Subscript[a, 1] Subscript[a, 3] Subscript[a, 4] + Subscript[a, 2] Subscript[a, 3] Subscript[a, 4]) z) Derivative[1][w][z] - Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] Subscript[a, 4] w[z] == 0 /; w[z] == Subscript[c, 1] HypergeometricPFQRegularized[ {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + Subscript[c, 2] z^(1 - Subscript[b, 1]) HypergeometricPFQRegularized[ {1 + Subscript[a, 1] - Subscript[b, 1], 1 + Subscript[a, 2] - Subscript[b, 1], 1 + Subscript[a, 3] - Subscript[b, 1], 1 + Subscript[a, 4] - Subscript[b, 1]}, {2 - Subscript[b, 1], 1 - Subscript[b, 1] + Subscript[b, 2], 1 - Subscript[b, 1] + Subscript[b, 3]}, z] + Subscript[c, 3] z^(1 - Subscript[b, 2]) HypergeometricPFQRegularized[{1 + Subscript[a, 1] - Subscript[b, 2], 1 + Subscript[a, 2] - Subscript[b, 2], 1 + Subscript[a, 3] - Subscript[b, 2], 1 + Subscript[a, 4] - Subscript[b, 2]}, {2 - Subscript[b, 2], 1 + Subscript[b, 1] - Subscript[b, 2], 1 - Subscript[b, 2] + Subscript[b, 3]}, z] + Subscript[c, 4] z^(1 - Subscript[b, 3]) HypergeometricPFQRegularized[ {1 + Subscript[a, 1] - Subscript[b, 3], 1 + Subscript[a, 2] - Subscript[b, 3], 1 + Subscript[a, 3] - Subscript[b, 3], 1 + Subscript[a, 4] - Subscript[b, 3]}, {2 - Subscript[b, 3], 1 + Subscript[b, 1] - Subscript[b, 3], 1 + Subscript[b, 2] - Subscript[b, 3]}, z] && !Element[Subscript[b, 1], Integers] && !Element[Subscript[b, 2], Integers] && !Element[Subscript[b, 3], Integers] && !Element[Subscript[b, 1] - Subscript[b, 2], Integers] && !Element[Subscript[b, 1] - Subscript[b, 3], Integers] && !Element[Subscript[b, 2] - Subscript[b, 3], Integers]










Standard Form





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MathML Form







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





2007-05-02





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