Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4953)

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=-17/3, b>=a

For fixed z and a=-17/3, b=6

http://functions.wolfram.com/07.23.03.4953.01

Input Form

Hypergeometric2F1[-(17/3), 6, 4/3, z] == (1/143489070) (3 (39766250 - 810437515 z + 4526902205 z^2 - 10249747508 z^3 + 10124502388 z^4 - 3632108480 z^5) - (1/z^(1/3)) (52360 (154 - 7854 z + 78540 z^2 - 301070 z^3 + 533715 z^4 - 442221 z^5 + 138736 z^6) Log[1 - z^(1/3)]) - (1/z^(1/3)) (52360 (-1)^(2/3) (154 - 7854 z + 78540 z^2 - 301070 z^3 + 533715 z^4 - 442221 z^5 + 138736 z^6) Log[1 + (-1)^(1/3) z^(1/3)]) + (1/z^(1/3)) (52360 (-1)^(1/3) (154 - 7854 z + 78540 z^2 - 301070 z^3 + 533715 z^4 - 442221 z^5 + 138736 z^6) 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]