Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4sh)

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=-47/8, b>=a

For fixed z and a=-47/8, b=-25/8

http://functions.wolfram.com/07.23.03.b4sh.01

Input Form

Hypergeometric2F1[-(47/8), -(25/8), 11/2, -z] == (1024 (Sqrt[z] Sqrt[1 + z] (15012928 + 336986616 z + 4163172063 z^2 + 43491748685 z^3 + 30713177256151 z^4 - 106167439075983 z^5 + 88323962254521 z^6 - 18414864794841 z^7 + 309869228925 z^8 + 10167665379 z^9 + 291396756 z^10) Cosh[ArcSinh[Sqrt[z]]/4] - (60051712 + 1389232016 z + 17574475329 z^2 + 185307519272 z^3 + 3102140078800 z^4 - 18755682478460 z^5 + 6057903271050 z^6 + 19286296989780 z^7 - 8155471944264 z^8 + 314916637020 z^9 + 10313363757 z^10 + 291396756 z^11) Sinh[ArcSinh[Sqrt[z]]/4]))/ (30686427408085251 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]