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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/07.27.13.0013.01









  


  










Input Form





Derivative[3][w][z] + (-3 (Log[r] + Log[s]) + (a r^z Log[r] (3 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3]) - Log[r] (1 + Subscript[b, 1] + Subscript[b, 2]))/ (-1 + a r^z)) Derivative[2][w][z] + (2 Log[r]^2 + 6 Log[r] Log[s] + 3 Log[s]^2 + (1/(-1 + a r^z)) (Log[r] (2 Log[s] - a r^z (Log[r] + 2 Log[s]) (3 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3]) + 2 Log[s] Subscript[b, 1] + 2 Log[s] Subscript[b, 2] - Log[r] Subscript[b, 1] Subscript[b, 2] + Log[r] (1 + a r^z ((1 + Subscript[a, 2]) (1 + Subscript[a, 3]) + Subscript[a, 1] (1 + Subscript[a, 2] + Subscript[a, 3])) + Subscript[b, 1] + Subscript[b, 2])))) Derivative[1][w][z] + ((-Log[s]) (3 Log[r]^2 + 6 Log[r] Log[s] + Log[s]^2) + (a r^z s^z Log[r]^3 Log[s] + 3 a r^z s^z Log[r]^2 Log[s]^2)/ (r^z s^z (a Log[r])) + (1/(-1 + a r^z)) (Log[r] (a r^z Subscript[a, 1] (Log[s] - Log[r] Subscript[a, 2]) (Log[s] - Log[r] Subscript[a, 3]) + Log[s] (a r^z (2 Log[r] + 3 Log[s] + Log[s] Subscript[a, 3] + Subscript[a, 2] (Log[s] - Log[r] Subscript[a, 3])) - (Log[r] + Log[s]) (1 + Subscript[b, 2]) - Subscript[b, 1] (Log[r] + Log[s] - Log[r] Subscript[b, 2]))))) w[z] == 0 /; w[z] == Subscript[c, 1] s^z HypergeometricPFQRegularized[ {Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, a r^z] + Subscript[c, 2] s^z (MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2]}}, a r^z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1]}}, a r^z]) + Subscript[c, 3] s^z MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {}}, (-a) r^z]










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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