Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5628)

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=6

http://functions.wolfram.com/07.23.03.5628.01

Input Form

Hypergeometric2F1[-(13/3), 6, 17/3, -z] == (1/(6973568802 z^(14/3))) (11 (3 z^(2/3) (-20020 + 73528 z - 260533 z^2 + 1181908 z^3 + 200386040 z^4 + 807136720 z^5 + 1232050820 z^6 + 836836000 z^7 + 213012800 z^8) - 3640 (1 + z)^4 (11 - 80 z + 380 z^2 - 1672 z^3 + 10450 z^4 + 58520 z^5) Log[1 + z^(1/3)] + 3640 (-1)^(1/3) (1 + z)^4 (11 - 80 z + 380 z^2 - 1672 z^3 + 10450 z^4 + 58520 z^5) Log[1 - (-1)^(1/3) z^(1/3)] - 3640 (-1)^(2/3) (1 + z)^4 (11 - 80 z + 380 z^2 - 1672 z^3 + 10450 z^4 + 58520 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]