Regularized hypergeometric function 2F1: Differentiation (formula 07.24.20.0032)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Differentiation

Symbolic differentiation

With respect to z

http://functions.wolfram.com/07.24.20.0032.02

Input Form

D[(1 - z^2)^(b + Floor[n/2] - 1/2) Hypergeometric2F1Regularized[ c - 1/2 + Floor[n/2], b, c, z^2], {z, n}] == (-1)^Floor[n/2] 2^(2 Floor[n/2]) Pochhammer[1/2, Floor[n/2]] Pochhammer[1/2 + n - 2 Floor[n/2], Floor[n/2]] Pochhammer[c - b, n - Floor[n/2]] z^(n - 2 Floor[n/2]) (1 - z^2)^(b - n + Floor[n/2] - 1/2) Hypergeometric2F1Regularized[c - 1/2, b, c + n - 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

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁},{b₁},z]
HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]