Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5051)

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=-16/3, b>=a

For fixed z and a=-16/3, b=4

http://functions.wolfram.com/07.23.03.5051.01

Input Form

Hypergeometric2F1[-(16/3), 4, 14/3, z] == (1/(2711943423 z^(11/3))) (11 (-3 z^(2/3) (145600 + 222040 z + 626080 z^2 - 77622377 z^3 + 313364752 z^4 - 534009320 z^5 + 468529360 z^6 - 209589380 z^7 + 38038000 z^8) - 7280 (-1 + z)^6 (40 + 285 z + 1254 z^2 + 5225 z^3) Log[1 - z^(1/3)] + 7280 (-1)^(1/3) (-1 + z)^6 (40 + 285 z + 1254 z^2 + 5225 z^3) Log[1 + (-1)^(1/3) z^(1/3)] - 7280 (-1)^(2/3) (-1 + z)^6 (40 + 285 z + 1254 z^2 + 5225 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]