Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b89g)

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=-43/8, b>=a

For fixed z and a=-43/8, b=41/8

http://functions.wolfram.com/07.23.03.b89g.01

Input Form

Hypergeometric2F1[-(43/8), 41/8, 3/2, -z] == -((1/(8545305 Sqrt[z] (1 + z)^(5/8))) (4 (Sqrt[z] (-1514385 - 5080885 z + 105822672 z^2 + 617535744 z^3 + 1242316800 z^4 + 1072889856 z^5 + 338690048 z^6) Cos[(5 ArcTan[Sqrt[z]])/4] - (497553 + 29631561 z + 292060460 z^2 + 1072164864 z^3 + 1806339072 z^4 + 1420492800 z^5 + 423362560 z^6) Sin[(5 ArcTan[Sqrt[z]])/4])))

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]