Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b0xq)

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=2, b>=a

For fixed z and a=2, b=14/5

http://functions.wolfram.com/07.23.03.b0xq.01

Input Form

Hypergeometric2F1[2, 14/5, 19/5, z] == -(14/(5 (-1 + z))) - (126/25) (-5 (1/(4 z^2) + 1/(9 z)) - (1/z^(14/5)) (Log[1 - z^(1/5)] + Log[1 - z^(1/5)/E^((2 I Pi)/5)]/E^((2 I Pi)/5) + E^((2 I Pi)/5) Log[1 - E^((2 I Pi)/5) z^(1/5)] + Log[1 - z^(1/5)/E^((4 I Pi)/5)]/E^((4 I Pi)/5) + E^((4 I Pi)/5) Log[1 - E^((4 I Pi)/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]
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