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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/07.25.13.0013.01









  


  








Input Form





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