Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5100)

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/07.23.03.5100.01

Input Form

Hypergeometric2F1[-(16/3), 6, 17/3, -z] == (1/(52301766015 z^(14/3))) (11 (3 z^(2/3) (-80080 + 323232 z - 1283100 z^2 + 6661200 z^3 + 1512544485 z^4 + 7644087600 z^5 + 15590254680 z^6 + 15907491600 z^7 + 8107799700 z^8 + 1650849200 z^9) - 7280 (1 + z)^5 (22 - 190 z + 1045 z^2 - 5225 z^3 + 36575 z^4 + 226765 z^5) Log[1 + z^(1/3)] + 7280 (-1)^(1/3) (1 + z)^5 (22 - 190 z + 1045 z^2 - 5225 z^3 + 36575 z^4 + 226765 z^5) Log[1 - (-1)^(1/3) z^(1/3)] - 7280 (-1)^(2/3) (1 + z)^5 (22 - 190 z + 1045 z^2 - 5225 z^3 + 36575 z^4 + 226765 z^5) 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]