Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4866)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=-17/3, b>=a

For fixed z and a=-17/3, b=4

http://functions.wolfram.com/07.23.03.4866.01

Input Form

Hypergeometric2F1[-(17/3), 4, 13/3, -z] == (1/(774840978 z^(10/3))) (3 z^(1/3) (366520 - 1034110 z + 5000380 z^2 + 168966134 z^3 + 648082024 z^4 + 1091630435 z^5 + 956865910 z^6 + 429325820 z^7 + 78278200 z^8) + 52360 (1 + z)^6 (-7 + 60 z - 345 z^2 + 2990 z^3) Log[1 + z^(1/3)] + 52360 (-1)^(2/3) (1 + z)^6 (-7 + 60 z - 345 z^2 + 2990 z^3) Log[1 - (-1)^(1/3) z^(1/3)] - 52360 (-1)^(1/3) (1 + z)^6 (-7 + 60 z - 345 z^2 + 2990 z^3) Log[1 + (-1)^(2/3) z^(1/3)])

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]