Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4910)

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/07.23.03.4910.01

Input Form

Hypergeometric2F1[-(17/3), 5, 10/3, z] == (1/(344373768 z^(7/3))) (-3 z^(1/3) (52360 + 850850 z - 82320576 z^2 + 532361392 z^3 - 1341438448 z^4 + 1637248767 z^5 - 973780808 z^6 + 227006780 z^7) - 52360 (-1 + z)^4 (1 + 20 z + 690 z^2 - 5980 z^3 + 8671 z^4) Log[1 - z^(1/3)] - 52360 (-1)^(2/3) (-1 + z)^4 (1 + 20 z + 690 z^2 - 5980 z^3 + 8671 z^4) Log[1 + (-1)^(1/3) z^(1/3)] + 52360 (-1)^(1/3) (-1 + z)^4 (1 + 20 z + 690 z^2 - 5980 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]