Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ap7p)

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=-26/5, b>=a

For fixed z and a=-26/5, b=3

http://functions.wolfram.com/07.23.03.ap7p.01

Input Form

Hypergeometric2F1[-(26/5), 3, 29/5, -z] == (1/(91552734375 z^(24/5))) (19 (-1)^(1/5) (144144 (-1)^(4/5) (1 + z)^8 (133 - 434 z + 558 z^2) Log[1 + z^(1/5)] + 144144 (1 + z)^8 (133 - 434 z + 558 z^2) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (144144 (1 + z)^8 (133 - 434 z + 558 z^2) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-144144 (1 + z)^8 (133 - 434 z + 558 z^2) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-4792788 - 20572552 z - 20468448 z^2 + 16144128 z^3 + 932807427 z^4 + 2307963762 z^5 + 2658590298 z^6 + 1681304352 z^7 + 567494928 z^8 + 80432352 z^9) + 144144 (1 + z)^8 (133 - 434 z + 558 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]