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

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=-35/8, b>=a

For fixed z and a=-35/8, b=41/8

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

Input Form

Hypergeometric2F1[-(35/8), 41/8, 17/4, z] == (8 2^(1/4) (-4788 - 30723 z - 233814 z^2 + 11677357 z^3 - 48177888 z^4 + 76860160 z^5 - 54579200 z^6 + 14483456 z^7 + (1/Sqrt[1 - z]) (4788 + 28329 z + 217854 z^2 + 25059817 z^3 - 161201732 z^4 + 388459520 z^5 - 452781056 z^6 + 258146304 z^7 - 57933824 z^8)))/(294865765 (1 + Sqrt[1 - z])^(1/4) z^3)

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]