Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aqv2)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 5 and fixed z

For fixed z and a=-21/5, b>=a

For fixed z and a=-21/5, b=3

http://functions.wolfram.com/07.23.03.aqv2.01

Input Form

Hypergeometric2F1[-(21/5), 3, 29/5, z] == -((1/(3662109375 z^(24/5))) (19 (-1)^(1/5) (11088 (-1)^(4/5) (-1 + z)^7 (133 + 364 z + 403 z^2) Log[1 - z^(1/5)] + 11088 (-1 + z)^7 (133 + 364 z + 403 z^2) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-11088 (-1 + z)^7 (133 + 364 z + 403 z^2) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (11088 (-1 + z)^7 (133 + 364 z + 403 z^2) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-368676 + 1407868 z - 1203048 z^2 - 892584 z^3 + 37049955 z^4 - 72983169 z^5 + 62925912 z^6 - 26498472 z^7 + 4468464 z^8) - 11088 (-1 + z)^7 (133 + 364 z + 403 z^2) Log[1 - (-1)^(4/5) z^(1/5)]))))))

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]