Gauss hypergeometric function 2F1: Differential equations (formula 07.23.13.0036)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,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/07.23.13.0036.01

Input Form

h[z]^2 Derivative[2][w][z] - (2 Derivative[1][h][z] + h[z] (((c - (1 + a + b) g[z]) Derivative[1][g][z])/((-1 + g[z]) g[z]) + Derivative[2][g][z]/Derivative[1][g][z])) h[z] Derivative[1][w][z] + ((a b h[z]^2 Derivative[1][g][z]^2)/((-1 + g[z]) g[z]) + 2 Derivative[1][h][z]^2 + h[z] (((c - (1 + a + b) g[z]) Derivative[1][g][z] Derivative[1][h][z])/ ((-1 + g[z]) g[z]) + (Derivative[1][h][z] Derivative[2][g][z])/ Derivative[1][g][z] - Derivative[2][h][z])) w[z] == 0 /; w[z] == Subscript[c, 1] h[z] Hypergeometric2F1Regularized[a, b, c, g[z]] + Subscript[c, 2] h[z] MeijerG[{{1 - a, 1 - b}, {}}, {{0, 1 - c}, {}}, 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},{b₁,b₂},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]