Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6144)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-8/3, b>=a

For fixed z and a=-8/3, b=-7/3

http://functions.wolfram.com/07.23.03.6144.01

Input Form

Hypergeometric2F1[-(8/3), -(7/3), 11/2, -z] == (6561 (3 Sqrt[z] (-774144 - 11104256 z - 81637376 z^2 - 458493952 z^3 + 12229328793 z^4 + 2120263429 z^5 - 9387726628 z^6 + 1108525424 z^7) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (6967296 + 97873920 z + 706654208 z^2 + 3929411584 z^3 + 31287517184 z^4 - 125716201369 z^5 + 62759413180 z^6 - 4471087408 z^7) Sinh[ArcSinh[Sqrt[z]]/3]))/ (311494317420715 z^(9/2) Sqrt[1 + z])

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]