Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bft0)

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=45/8

http://functions.wolfram.com/07.23.03.bft0.01

Input Form

Hypergeometric2F1[-(31/8), 45/8, 11/2, -z] == (1024 (4 Sqrt[z] (399280 - 1162190 z + 3649134 z^2 - 15802219 z^3 + 6339224247 z^4 + 26475882048 z^5 + 40988842752 z^6 + 28044656640 z^7 + 7169310720 z^8) Cos[ArcTan[Sqrt[z]]/4] - (6388480 - 16598640 z + 52051139 z^2 - 232793074 z^3 + 2620619379 z^4 + 17815230048 z^5 + 33513123072 z^6 + 25804247040 z^7 + 7169310720 z^8) Sin[ArcTan[Sqrt[z]]/4]))/(25272884139789 z^(9/2) (1 + z)^(1/8))

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]