Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4945)

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/07.23.03.4945.01

Input Form

Hypergeometric2F1[-(17/3), 6, -(8/3), z] == (1/393660) ((1/(-1 + z)^3) (3 (-131220 - 1279395 z - 11770434 z^2 - 196173900 z^3 + 3139413290 z^4 - 11670390095 z^5 + 18411032640 z^6 - 13302597308 z^7 + 3632108480 z^8)) + 15655640 z^(11/3) (119 - 493 z + 464 z^2) Log[1 - z^(1/3)] + 15655640 (-1)^(2/3) z^(11/3) (119 - 493 z + 464 z^2) Log[1 + (-1)^(1/3) z^(1/3)] - 15655640 (-1)^(1/3) z^(11/3) (119 - 493 z + 464 z^2) 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]