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

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=35/8, b>=a

For fixed z and a=35/8, b=45/8

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

Input Form

Hypergeometric2F1[35/8, 45/8, -(5/2), z] == (1/(206016 (1 - z)^(25/2))) (2 Sqrt[1 - z] (103008 - 2279052 z + 31626675 z^2 - 632591442 z^3 - 5626763295 z^4 - 8060032552 z^5 - 2765004827 z^6 - 165879450 z^7 + 1105863 z^8) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (154512 - 3441111 z + 47924472 z^2 - 3238758269 z^3 - 16868078610 z^4 - 19566481233 z^5 - 5959906916 z^6 - 332864763 z^7 + 2211726 z^8) Sin[(3 ArcSin[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]