Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5go)

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=29/8

http://functions.wolfram.com/07.23.03.b5go.01

Input Form

Hypergeometric2F1[-(47/8), 29/8, -(7/2), -z] == (1/(8960 (1 + z)^(9/8))) ((8960 - 44720 z + 186723 z^2 - 925140 z^3 + 10053120 z^4 + 80980992 z^5 + 136642560 z^6 + 66846720 z^7) Cos[ArcTan[Sqrt[z]]/4] - Sqrt[z] (-2240 + 11880 z - 50577 z^2 + 248160 z^3 + 12572928 z^4 + 28938240 z^5 + 16711680 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]