Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4915)

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=5

http://functions.wolfram.com/07.23.03.4915.01

Input Form

Hypergeometric2F1[-(17/3), 5, 16/3, -z] == (1/(27894275208 z^(13/3))) (13 (3 z^(1/3) (-366520 + 824670 z - 2591820 z^2 + 13296822 z^3 + 469754928 z^4 + 1830299985 z^5 + 3113978910 z^6 + 2748919635 z^7 + 1239926688 z^8 + 227006780 z^9) + 52360 (1 + z)^6 (7 - 56 z + 276 z^2 - 1196 z^3 + 8671 z^4) Log[1 + z^(1/3)] + 52360 (-1)^(2/3) (1 + z)^6 (7 - 56 z + 276 z^2 - 1196 z^3 + 8671 z^4) Log[1 - (-1)^(1/3) z^(1/3)] - 52360 (-1)^(1/3) (1 + z)^6 (7 - 56 z + 276 z^2 - 1196 z^3 + 8671 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]