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

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=-19/8, b>=a

For fixed z and a=-19/8, b=1/8

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

Input Form

Hypergeometric2F1[-(19/8), 1/8, 9/2, -z] == -((256 (Sqrt[z] (-400 - 3185 z - 12340 z^2 - 89798 z^3 + 26316 z^4 + 3951 z^5 + 432 z^6) Cos[(5 ArcTan[Sqrt[z]])/4] + 4 (80 + 622 z + 2351 z^2 + 8326 z^3 - 20368 z^4 - 1260 z^5 - 135 z^6) Sin[(5 ArcTan[Sqrt[z]])/4]))/(11762361 z^(7/2) (1 + z)^(5/8)))

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]