Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5605)

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=-13/3, b>=a

For fixed z and a=-13/3, b=5

http://functions.wolfram.com/07.23.03.5605.01

Input Form

Hypergeometric2F1[-(13/3), 5, 17/3, z] == (1/(2324522934 z^(14/3))) (11 (3 z^(2/3) (-100100 - 121940 z - 221585 z^2 - 639275 z^3 + 66142816 z^4 - 218951720 z^5 + 284598340 z^6 - 168508340 z^7 + 38038000 z^8) + 3640 (-1 + z)^5 (55 + 320 z + 1140 z^2 + 3344 z^3 + 10450 z^4) Log[1 - z^(1/3)] - 3640 (-1)^(1/3) (-1 + z)^5 (55 + 320 z + 1140 z^2 + 3344 z^3 + 10450 z^4) Log[1 + (-1)^(1/3) z^(1/3)] + 3640 (-1)^(2/3) (-1 + z)^5 (55 + 320 z + 1140 z^2 + 3344 z^3 + 10450 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]