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

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=-21/8, b>=a

For fixed z and a=-21/8, b=21/8

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

Input Form

Hypergeometric2F1[-(21/8), 21/8, -(11/2), z] == -((1/(135168 (1 - z)^(11/2))) (Sqrt[1 - z] (-135168 + 544512 z - 747360 z^2 + 319907 z^3 + 49220 z^4 + 32591 z^5 + 52026 z^6 - 104880 z^7 + 37536 z^8) Cos[(3 ArcSin[Sqrt[z]])/4] + 2 Sqrt[z] (-50688 + 211584 z - 305418 z^2 + 145521 z^3 + 15755 z^4 + 8671 z^5 + 49887 z^6 - 61824 z^7 + 18768 z^8) Sin[(3 ArcSin[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]