Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5403)

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=-14/3, b>=a

For fixed z and a=-14/3, b=4

http://functions.wolfram.com/07.23.03.5403.01

Input Form

Hypergeometric2F1[-(14/3), 4, 16/3, z] == (1/(774840978 z^(13/3))) (13 (3 z^(1/3) (215600 - 140140 z - 239470 z^2 - 708400 z^3 + 11909918 z^4 - 28904638 z^5 + 30440795 z^6 - 15289120 z^7 + 3010700 z^8) + 3080 (-1 + z)^6 (70 + 357 z + 1020 z^2 + 1955 z^3) Log[1 - z^(1/3)] + 3080 (-1)^(2/3) (-1 + z)^6 (70 + 357 z + 1020 z^2 + 1955 z^3) Log[1 + (-1)^(1/3) z^(1/3)] - 3080 (-1)^(1/3) (-1 + z)^6 (70 + 357 z + 1020 z^2 + 1955 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]