Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4m2)

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=-43/8

http://functions.wolfram.com/07.23.03.b4m2.01

Input Form

Hypergeometric2F1[-(47/8), -(43/8), 5/4, z] == (1/(392637525 z)) (2^(1/4) (1 + Sqrt[1 - z])^(3/4) (82135461 + 3855856722 z + 27338999739 z^2 + 53548406012 z^3 + 33385150155 z^4 + 6193427730 z^5 + 233961845 z^6 + (1/Sqrt[1 - z]) (-82135461 - 3618470229 z - 20502651321 z^2 - 17461348825 z^3 + 20570637521 z^4 + 18399536225 z^5 + 2654983245 z^6 + 39448845 z^7)))

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]