Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5045)

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/07.23.03.5045.01

Input Form

Hypergeometric2F1[-(16/3), 4, 5/3, z] == (1/7971615) (7818735 - 92925024 z + 343625880 z^2 - 554090160 z^3 + 409669260 z^4 - 114114000 z^5 - (7280 (-1 + z)^3 (-14 + 798 z - 4389 z^2 + 5225 z^3) Log[1 - z^(1/3)])/ z^(2/3) + (7280 (-1)^(1/3) (-1 + z)^3 (-14 + 798 z - 4389 z^2 + 5225 z^3) Log[1 + (-1)^(1/3) z^(1/3)])/z^(2/3) - (7280 (-1)^(2/3) (-1 + z)^3 (-14 + 798 z - 4389 z^2 + 5225 z^3) Log[1 - (-1)^(2/3) z^(1/3)])/z^(2/3))

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]