Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bof0)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-17/8, b>=a

For fixed z and a=-17/8, b=6

http://functions.wolfram.com/07.23.03.bof0.01

Input Form

Hypergeometric2F1[-(17/8), 6, -(1/8), -z] == (1/83886080) (51 ((256 (82255 + 226135 z + 210945 z^2 + 66297 z^3))/ (1 + z)^4 + (9392075/3) (8 - 72 z - 9 (-1)^(1/8) z^(9/8) Log[1 - (-1)^(1/8) z^(1/8)] + 9 (-1)^(1/8) z^(9/8) Log[1 + (-1)^(1/8) z^(1/8)] - 9 (-1)^(3/8) z^(9/8) Log[1 - (-1)^(3/8) z^(1/8)] + 9 (-1)^(3/8) z^(9/8) Log[1 + (-1)^(3/8) z^(1/8)] - 9 (-1)^(5/8) z^(9/8) Log[1 - (-1)^(5/8) z^(1/8)] + 9 (-1)^(5/8) z^(9/8) Log[1 + (-1)^(5/8) z^(1/8)] - 9 (-1)^(7/8) z^(9/8) Log[1 - (-1)^(7/8) z^(1/8)] + 9 (-1)^(7/8) z^(9/8) Log[1 + (-1)^(7/8) z^(1/8)]) + 94473225 (-(8/17) + (8 z)/9 - 8 z^2 + (-1)^(1/8) z^(17/8) (-Log[1 - (-1)^(1/8) z^(1/8)] + Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] - I Log[1 - (-1)^(5/8) z^(1/8)] + I Log[1 + (-1)^(5/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)]))))

Standard Form

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MathML Form

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⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 8 </mn> </mroot> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mroot> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 8 </mn> </mrow> </msup> <mo> ⁢ </mo> 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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]