Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b64u)

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=-45/8, b>=a

For fixed z and a=-45/8, b=-43/8

http://functions.wolfram.com/07.23.03.b64u.01

Input Form

Hypergeometric2F1[-(45/8), -(43/8), 5/2, -z] == (1/(8992509295 z^(3/2) Sqrt[1 + z])) (16 (Sqrt[z] Sqrt[1 + z] (1245753 + 683985859 z - 11039569947 z^2 + 42397920471 z^3 - 52599062053 z^4 + 21839939001 z^5 - 2591045433 z^6 + 47552109 z^7) Cosh[(3 ArcSinh[Sqrt[z]])/4] + (-1661004 - 164024145 z + 5307064809 z^2 - 23007844741 z^3 + 13679005813 z^4 + 22566170285 z^5 - 17093077989 z^6 + 2449478121 z^7 - 47552109 z^8) Sinh[(3 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]