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

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=-29/8, b>=a

For fixed z and a=-29/8, b=47/8

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

Input Form

Hypergeometric2F1[-(29/8), 47/8, -(21/4), z] == (1/(16290624 2^(1/4) (-1 + z)^7)) ((1 + Sqrt[1 - z])^(1/4) (-8145312 + 23466256 z - 8620170 z^2 - 9925673 z^3 - 14648585 z^4 - 33883899 z^5 + 434024807 z^6 - 881744160 z^7 + 798107904 z^8 - 350760960 z^9 + 61276160 z^10 + (1/Sqrt[1 - z]) (2 (-4072656 + 13769456 z - 9667567 z^2 - 4019894 z^3 - 4878346 z^4 - 12737032 z^5 - 568001983 z^6 + 1974267606 z^7 - 2808187008 z^8 + 2068459008 z^9 - 785776640 z^10 + 122552320 z^11))))

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]