Generalized hypergeometric function 1F2: Differential equations (formula 07.22.13.0007)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Differential equations

Ordinary linear differential equations and wronskians

For the direct function itself

http://functions.wolfram.com/07.22.13.0007.01

Input Form

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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]