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

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=27/8, b>=a

For fixed z and a=27/8, b=45/8

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

Input Form

Hypergeometric2F1[27/8, 45/8, -(11/2), z] == (1/(48345088 (1 - z)^(29/2))) (Sqrt[1 - z] (48345088 - 857301248 z + 7506433312 z^2 - 44384058069 z^3 + 210314913339 z^4 - 973786227789 z^5 + 7841155746767 z^6 + 28457431422437 z^7 + 16083540412001 z^8 + 1575010264289 z^9 - 21382598347 z^10 + 523441820 z^11) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (36258816 - 648263680 z + 5720287468 z^2 - 34052812767 z^3 + 162117558125 z^4 - 750644282951 z^5 + 15296593048665 z^6 + 36817323435863 z^7 + 17785867239463 z^8 + 1585636133235 z^9 - 21644319257 z^10 + 523441820 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]