Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b13m)

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=21/5

http://functions.wolfram.com/07.23.03.b13m.01

Input Form

Hypergeometric2F1[2, 21/5, 26/5, z] == -(21/(5 (-1 + z))) - (336/25) (-5 (1/z^4 + 1/(6 z^3) + 1/(11 z^2) + 1/(16 z)) - (1/z^(21/5)) (Log[1 - z^(1/5)] + E^((2 I Pi)/5) Log[1 - z^(1/5)/E^((2 I Pi)/5)] + Log[1 - E^((2 I Pi)/5) z^(1/5)]/ E^((2 I Pi)/5) + E^((4 I Pi)/5) Log[1 - z^(1/5)/E^((4 I Pi)/5)] + Log[1 - E^((4 I Pi)/5) z^(1/5)]/E^((4 I Pi)/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]