Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5088)

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=-16/3, b>=a

For fixed z and a=-16/3, b=6

http://functions.wolfram.com/07.23.03.5088.01

Input Form

Hypergeometric2F1[-(16/3), 6, -(1/3), -z] == (1/531441) (-((1/(1 + z)) (3 (-177147 + 16828965 z + 378720920 z^2 + 2118716600 z^3 + 4752848100 z^4 + 4646341700 z^5 + 1650849200 z^6))) + 138320 z^(4/3) (364 + 4576 z + 17160 z^2 + 24640 z^3 + 11935 z^4) Log[1 + z^(1/3)] - 138320 (-1)^(1/3) z^(4/3) (364 + 4576 z + 17160 z^2 + 24640 z^3 + 11935 z^4) Log[1 - (-1)^(1/3) z^(1/3)] + 138320 (-1)^(2/3) z^(4/3) (364 + 4576 z + 17160 z^2 + 24640 z^3 + 11935 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]