Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5097)

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/07.23.03.5097.01

Input Form

Hypergeometric2F1[-(16/3), 6, 14/3, z] == (1/(24407490807 z^(11/3))) (11 (-3 z^(2/3) (29120 + 240968 z + 1933568 z^2 - 711000325 z^3 + 4415540720 z^4 - 10662051400 z^5 + 12560147600 z^6 - 7255748500 z^7 + 1650849200 z^8) - 7280 (-1 + z)^4 (8 + 95 z + 836 z^2 + 10450 z^3 - 146300 z^4 + 226765 z^5) Log[1 - z^(1/3)] + 7280 (-1)^(1/3) (-1 + z)^4 (8 + 95 z + 836 z^2 + 10450 z^3 - 146300 z^4 + 226765 z^5) Log[1 + (-1)^(1/3) z^(1/3)] - 7280 (-1)^(2/3) (-1 + z)^4 (8 + 95 z + 836 z^2 + 10450 z^3 - 146300 z^4 + 226765 z^5) Log[1 - (-1)^(2/3) z^(1/3)]))

Standard Form

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MathML Form

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</apply> <cn type='integer'> 29120 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]