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

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-25/8, b>=a

For fixed z and a=-25/8, b=35/8

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

Input Form

Hypergeometric2F1[-(25/8), 35/8, -(17/4), z] == (-4434144 + 8737872 z + 665874 z^2 - 262713 z^3 - 2244660 z^4 - 29006901 z^5 + 64567328 z^6 - 48038144 z^7 + 12300288 z^8 - (1/Sqrt[1 - z]) (2 (2217072 - 5477472 z + 1574397 z^2 + 705375 z^3 + 1284723 z^4 + 14056713 z^5 - 55180328 z^6 + 70125888 z^7 - 39029760 z^8 + 8200192 z^9)))/(4434144 2^(1/4) (1 + Sqrt[1 - z])^(3/4) (-1 + z)^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]