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

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=-15/8, b>=a

For fixed z and a=-15/8, b=13/8

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

Input Form

Hypergeometric2F1[-(15/8), 13/8, 11/2, -z] == (1/(10541751 z^(9/2) (1 + z)^(1/8))) (1024 (2 Sqrt[z] (-224 - 1124 z - 2133 z^2 - 1610 z^3 + 5819 z^4 + 3588 z^5 + 736 z^6) Cos[ArcTan[Sqrt[z]]/4] + (1792 + 9552 z + 19727 z^2 + 17551 z^3 - 2415 z^4 - 1679 z^5 - 368 z^6) Sin[ArcTan[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]