Gauss hypergeometric function 2F1: Differentiation (formula 07.23.20.0041)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Differentiation

Symbolic differentiation

With respect to z

http://functions.wolfram.com/07.23.20.0041.02

Input Form

D[(1 - z^2)^(a + b - 1/2) Hypergeometric2F1[a, b, 1/2, z^2], {z, n}] == 2^(2 n - 2 Floor[n/2]) Pochhammer[1/2 - a, n - Floor[n/2]] Pochhammer[1/2 - b, n - Floor[n/2]] z^(n - 2 Floor[n/2]) (1 - z^2)^(a + b - n - 1/2) Hypergeometric2F1[a - Floor[n/2], b - Floor[n/2], 1/2 + n - 2 Floor[n/2], z^2] /; Element[n, Integers] && n >= 0

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)

2001-10-29

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]