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

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.blpm.01

Input Form

Hypergeometric2F1[-(21/8), 21/8, 11/2, z] == (1/(5098555 z^(9/2))) (1024 (-2 Sqrt[z] (-672 + 2516 z - 2583 z^2 - 525 z^3 - 3473 z^4 + 6129 z^5 - 3744 z^6 + 816 z^7) Cos[(3 ArcSin[Sqrt[z]])/4] - (1/Sqrt[1 - z]) ((1792 - 8240 z + 12559 z^2 - 4291 z^3 + 1295 z^4 - 12241 z^5 + 15798 z^6 - 8304 z^7 + 1632 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]