html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.28.13.0007.01

 Input Form

 Derivative[4][w][z] + (((6 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4]) Derivative[1][g][z])/(-1 + g[z]) - ((3 + Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]) Derivative[1][g][z])/((-1 + g[z]) g[z]) - (6 Derivative[2][g][z])/ Derivative[1][g][z]) Derivative[3][w][z] + (((7 + Subscript[a, 1] Subscript[a, 2] + 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] + 3 (Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4])) Derivative[1][g][z]^2)/((-1 + g[z]) g[z]) - (((1 + Subscript[b, 2]) (1 + Subscript[b, 3]) + Subscript[b, 1] (1 + Subscript[b, 2] + Subscript[b, 3])) Derivative[1][g][z]^2)/ ((-1 + g[z]) g[z]^2) - (3 (6 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4]) Derivative[2][g][z])/(-1 + g[z]) + (3 (3 + Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]) Derivative[2][g][z])/((-1 + g[z]) g[z]) + (15 Derivative[2][g][z]^2)/ Derivative[1][g][z]^2 - (4 Derivative[3][g][z])/Derivative[1][g][z]) Derivative[2][w][z] + ((Subscript[b, 1] Subscript[b, 2] Subscript[b, 3] Derivative[1][g][z]^3)/ ((1 - g[z]) g[z]^3) + (3 (6 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4]) Derivative[2][g][z]^2)/ ((-1 + g[z]) Derivative[1][g][z]) - (3 (3 + Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]) Derivative[2][g][z]^2)/((-1 + g[z]) g[z] Derivative[1][g][z]) - (15 Derivative[2][g][z]^3)/Derivative[1][g][z]^3 + (1/((-1 + g[z]) g[z]^2)) (Derivative[1][g][z] ((1 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 1] Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 1] Subscript[a, 3] + Subscript[a, 2] Subscript[a, 3] + Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] + Subscript[a, 4] + Subscript[a, 1] Subscript[a, 4] + Subscript[a, 2] Subscript[a, 4] + Subscript[a, 1] Subscript[a, 2] Subscript[a, 4] + Subscript[a, 3] Subscript[a, 4] + Subscript[a, 1] Subscript[a, 3] Subscript[a, 4] + Subscript[a, 2] Subscript[a, 3] Subscript[a, 4]) Derivative[1][g][z]^2 + ((1 + Subscript[b, 2]) (1 + Subscript[b, 3]) + Subscript[b, 1] (1 + Subscript[b, 2] + Subscript[b, 3])) Derivative[2][g][z])) - ((6 + Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4]) Derivative[3][g][z])/(-1 + g[z]) + (10 Derivative[2][g][z] Derivative[3][g][z])/Derivative[1][g][z]^2 + (1/((-1 + g[z]) g[z])) ((-7 - Subscript[a, 1] Subscript[a, 2] - 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] - 3 (Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4])) Derivative[1][g][z] Derivative[2][g][z] + (3 + Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]) Derivative[3][g][z]) - Derivative[4][g][z]/Derivative[1][g][z]) Derivative[1][w][z] + ((Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] Subscript[a, 4] Derivative[1][g][z]^4)/((-1 + g[z]) g[z]^3)) 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]}, g[z]] + Subscript[c, 2] (MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2], 1 - Subscript[b, 3]}}, g[z]] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1], 1 - Subscript[b, 3]}}, g[z]] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 3]}, {1 - Subscript[b, 1], 1 - Subscript[b, 2]}}, g[z]]) + Subscript[c, 3] (MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {1 - Subscript[b, 3]}}, -g[z]] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 3]}, {1 - Subscript[b, 2]}}, -g[z]] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 2], 1 - Subscript[b, 3]}, {1 - Subscript[b, 1]}}, -g[z]]) + Subscript[c, 4] MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3], 1 - Subscript[a, 4]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2], 1 - Subscript[b, 3]}, {}}, g[z]]

 Standard Form

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 MathML Form

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

 2007-05-02