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

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=-16/5, b>=a

For fixed z and a=-16/5, b=6

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

Input Form

Hypergeometric2F1[-(16/5), 6, 24/5, -z] == (1/(30517578125 z^(19/5))) (57 (-1)^(1/5) (3696 (-1)^(4/5) (1 + z)^2 (-6 + 45 z - 260 z^2 + 2015 z^3 + 36270 z^4 + 49569 z^5) Log[1 + z^(1/5)] + 3696 (1 + z)^2 (-6 + 45 z - 260 z^2 + 2015 z^3 + 36270 z^4 + 49569 z^5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (3696 (1 + z)^2 (-6 + 45 z - 260 z^2 + 2015 z^3 + 36270 z^4 + 49569 z^5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-3696 (1 + z)^2 (-6 + 45 z - 260 z^2 + 2015 z^3 + 36270 z^4 + 49569 z^5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (5544 - 32956 z + 177760 z^2 + 105574105 z^3 + 392006160 z^4 + 469933464 z^5 + 183207024 z^6) + 3696 (1 + z)^2 (-6 + 45 z - 260 z^2 + 2015 z^3 + 36270 z^4 + 49569 z^5) Log[1 + (-1)^(4/5) 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]
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]