Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm50)

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=45/8

http://functions.wolfram.com/07.23.03.bm50.01

Input Form

Hypergeometric2F1[-(21/8), 45/8, -(11/2), z] == (1/(48345088 (1 - z)^(17/2))) (Sqrt[1 - z] (48345088 - 270567680 z + 538972192 z^2 - 358413117 z^3 - 83217588 z^4 - 79811886 z^5 - 245309260 z^6 + 1327748531 z^7 - 1931280376 z^8 + 1367880656 z^9 - 492347200 z^10 + 72569600 z^11) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (36258816 - 208213504 z + 430517644 z^2 - 311621733 z^3 - 48666988 z^4 - 43879262 z^5 - 736018032 z^6 + 2150340587 z^7 - 2558212904 z^8 + 1604983056 z^9 - 528632000 z^10 + 72569600 z^11) 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]