Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bl6g)

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=-21/8, b>=a

For fixed z and a=-21/8, b=-17/8

http://functions.wolfram.com/07.23.03.bl6g.01

Input Form

Hypergeometric2F1[-(21/8), -(17/8), 23/4, z] == (1/(255052221 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (336 - 4564 z + 31213 z^2 - 156245 z^3 + 881586 z^4 + 10706818 z^5 + 7696225 z^6 + 767575 z^7 + (1/Sqrt[1 - z]) (-336 + 4732 z - 33453 z^2 + 171302 z^3 - 956079 z^4 - 2313392 z^5 + 2003813 z^6 + 1089902 z^7 + 33511 z^8)))

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]