Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.by5m)

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=1/8, b>=a

For fixed z and a=1/8, b=45/8

http://functions.wolfram.com/07.23.03.by5m.01

Input Form

Hypergeometric2F1[1/8, 45/8, -(15/4), z] == (1/(17185168 2^(3/4) (-1 + z)^9)) ((1 + Sqrt[1 - z])^(3/4) (-8592584 + 77333256 z - 311969385 z^2 + 751516324 z^3 + 1605939810 z^4 - 1009804788 z^5 + 422152327 z^6 - 104212080 z^7 + 11499264 z^8 + (1/Sqrt[1 - z]) (4 (-2148146 + 20407387 z - 87390485 z^2 + 224592849 z^3 - 1132489272 z^4 + 818695833 z^5 - 455704681 z^6 + 170260835 z^7 - 38011456 z^8 + 3833088 z^9))))

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]