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

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=-31/8, b>=a

For fixed z and a=-31/8, b=-25/8

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

Input Form

Hypergeometric2F1[-(31/8), -(25/8), 9/2, -z] == (256 (Sqrt[z] Sqrt[1 + z] (285200 + 5529315 z + 65774250 z^2 + 42437856757 z^3 - 118886656324 z^4 + 69675327261 z^5 - 8319645846 z^6 + 55447275 z^7) Cosh[ArcSinh[Sqrt[z]]/4] - (1140800 + 22901560 z + 278209035 z^2 + 4555677850 z^3 - 22371353467 z^4 - 2009193916 z^5 + 20283608997 z^6 - 4322332854 z^7 + 55447275 z^8) Sinh[ArcSinh[Sqrt[z]]/4]))/ (10583990987427 z^(7/2) 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]