Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5073)

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=5

http://functions.wolfram.com/07.23.03.5073.01

Input Form

Hypergeometric2F1[-(16/3), 5, 11/3, -z] == (1/(301327047 z^(8/3))) (3 z^(2/3) (-18200 + 211120 z + 96789063 z^2 + 639223760 z^3 + 1607367320 z^4 + 1949067120 z^5 + 1150649500 z^6 + 266266000 z^7) - 7280 (1 + z)^4 (5 - 76 z + 1254 z^2 + 20900 z^3 + 36575 z^4) Log[1 + z^(1/3)] + 7280 (-1)^(1/3) (1 + z)^4 (5 - 76 z + 1254 z^2 + 20900 z^3 + 36575 z^4) Log[1 - (-1)^(1/3) z^(1/3)] - 7280 (-1)^(2/3) (1 + z)^4 (5 - 76 z + 1254 z^2 + 20900 z^3 + 36575 z^4) 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]