Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5lt)

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=37/8

http://functions.wolfram.com/07.23.03.b5lt.01

Input Form

Hypergeometric2F1[-(47/8), 37/8, -(5/2), -z] == (1/(9280 (1 + z)^(9/8))) ((-(-9280 + 90712 z - 812145 z^2 + 14776080 z^3 + 197338368 z^4 + 599408640 z^5 + 685178880 z^6 + 267386880 z^7)) Cos[ArcTan[Sqrt[z]]/4] + Sqrt[z] (2320 - 23403 z + 210540 z^2 + 24978432 z^3 + 108334080 z^4 + 150405120 z^5 + 66846720 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]