Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.0657)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

Values at fixed points

For z==-8 and integer parameters

http://functions.wolfram.com/07.23.03.0657.01

Input Form

Hypergeometric2F1[-n, 8/3 - 2 n, -(1/3), -8] == 2^(2 n) Pochhammer[4 - 3 n, n] ((Pochhammer[-(5/6), n] + (n/3 - 3/4) Pochhammer[-(1/2), n - 1])/(Pochhammer[-(1/3), n] Pochhammer[-(2/3), n])) /; Element[n - 1, Integers] && n - 1 > 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]