Gauss hypergeometric function 2F1: Differential equations (formula 07.23.13.0040)

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/07.23.13.0040.01

Input Form

(1 - d r^z) Derivative[2][w][z] - ((1 - c + (a + b) d r^z) Log[r] + 2 (1 - d r^z) Log[s]) Derivative[1][w][z] + ((-a) b d r^z Log[r]^2 + (1 - c + (a + b) d r^z) Log[r] Log[s] + (1 - d r^z) Log[s]^2) w[z] == 0 /; w[z] == Subscript[c, 1] s^z Hypergeometric2F1Regularized[a, b, c, d r^z] + Subscript[c, 2] s^z MeijerG[{{1 - a, 1 - b}, {}}, {{0, 1 - c}, {}}, d 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

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]