Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.avvi)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 5 and fixed z

For fixed z and a=-6/5, b>=a

For fixed z and a=-6/5, b=4

http://functions.wolfram.com/07.23.03.avvi.01

Input Form

Hypergeometric2F1[-(6/5), 4, 19/5, z] == (1/(390625 z^(14/5))) (21 (-1)^(1/5) (12 (-1)^(4/5) (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 - z^(1/5)] + 12 (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-12 (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (12 (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (9 + 28 z - 3608 z^2 + 3696 z^3) - 12 (3 + 8 z + 33 z^2 - 352 z^3 + 308 z^4) Log[1 - (-1)^(4/5) z^(1/5)])))))

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]