Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b8qc)

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=-41/8, b>=a

For fixed z and a=-41/8, b=-29/8

http://functions.wolfram.com/07.23.03.b8qc.01

Input Form

Hypergeometric2F1[-(41/8), -(29/8), 23/4, z] == (16 2^(3/4) (7847400 - 171596480 z + 2027845445 z^2 - 19323598275 z^3 + 9224956604857 z^4 + 32380592707505 z^5 + 29268420173487 z^6 + 7843457186487 z^7 + 482624389035 z^8 - 842925861 z^9 + (1/Sqrt[1 - z]) (4 (-1961850 + 43880045 z - 528165690 z^2 + 5079140475 z^3 + 2184346311883 z^4 + 4485093191241 z^5 - 1695511598553 z^6 - 4005679457799 z^7 - 944462835765 z^8 - 28659479274 z^9 + 280975287 z^10))))/ (287548169425389 (1 + Sqrt[1 - z])^(3/4) 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]