Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5085)

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=6

http://functions.wolfram.com/07.23.03.5085.01

Input Form

Hypergeometric2F1[-(16/3), 6, -(4/3), z] == (1/177147) ((1/(-1 + z)^2) (3 (59049 + 1299078 z + 61706205 z^2 - 908180240 z^3 + 3772228460 z^4 - 6721314600 z^5 + 5445139700 z^6 - 1650849200 z^7)) - 1521520 z^(7/3) (-104 + 780 z - 1680 z^2 + 1085 z^3) Log[1 - z^(1/3)] + 1521520 (-1)^(1/3) z^(7/3) (-104 + 780 z - 1680 z^2 + 1085 z^3) Log[1 + (-1)^(1/3) z^(1/3)] - 1521520 (-1)^(2/3) z^(7/3) (-104 + 780 z - 1680 z^2 + 1085 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]