Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bm6m)

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=47/8

http://functions.wolfram.com/07.23.03.bm6m.01

Input Form

Hypergeometric2F1[-(21/8), 47/8, -(21/4), z] == (1/(775744 2^(1/4) (-1 + z)^8)) ((1 + Sqrt[1 - z])^(1/4) (2 (193936 - 969680 z + 1565035 z^2 - 442060 z^3 - 529046 z^4 - 938308 z^5 + 6835475 z^6 - 10683480 z^7 + 7930560 z^8 - 2962432 z^9 + 450560 z^10) + (1/Sqrt[1 - z]) (387872 - 2133296 z + 4051266 z^2 - 2230977 z^3 - 901232 z^4 - 1367534 z^5 - 40083322 z^6 + 109088007 z^7 - 127284384 z^8 + 79442176 z^9 - 26177536 z^10 + 3604480 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]