Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bph8)

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=-15/8, b>=a

For fixed z and a=-15/8, b=47/8

http://functions.wolfram.com/07.23.03.bph8.01

Input Form

Hypergeometric2F1[-(15/8), 47/8, -(11/2), -z] == (1/(96374784 (1 + z)^(19/2))) (Sqrt[1 + z] (96374784 + 677361408 z + 1881384544 z^2 + 2371668299 z^3 + 751567596 z^4 - 756406014 z^5 + 2145031980 z^6 + 6487844011 z^7 + 7088241248 z^8 + 4086762592 z^9 + 1249050880 z^10 + 160592256 z^11) Cosh[ArcSinh[Sqrt[z]]/4] - 4 Sqrt[z] (6023424 + 44217408 z + 130016263 z^2 + 179818600 z^3 + 80640300 z^4 - 45158568 z^5 + 1178486659 z^6 + 2398227964 z^7 + 2246382050 z^8 + 1172803500 z^9 + 332336752 z^10 + 40148064 z^11) Sinh[ArcSinh[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]