Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4962)

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=-17/3, b>=a

For fixed z and a=-17/3, b=6

http://functions.wolfram.com/07.23.03.4962.01

Input Form

Hypergeometric2F1[-(17/3), 6, 16/3, -z] == (1/(209207064060 z^(13/3))) (13 (3 z^(1/3) (-366520 + 1924230 z - 9935310 z^2 + 71769852 z^3 + 3652124640 z^4 + 17359730625 z^5 + 34688395875 z^6 + 35107772700 z^7 + 17842732908 z^8 + 3632108480 z^9) + 52360 (1 + z)^5 (7 - 70 z + 460 z^2 - 2990 z^3 + 43355 z^4 + 138736 z^5) Log[1 + z^(1/3)] + 52360 (-1)^(2/3) (1 + z)^5 (7 - 70 z + 460 z^2 - 2990 z^3 + 43355 z^4 + 138736 z^5) Log[1 - (-1)^(1/3) z^(1/3)] - 52360 (-1)^(1/3) (1 + z)^5 (7 - 70 z + 460 z^2 - 2990 z^3 + 43355 z^4 + 138736 z^5) Log[1 + (-1)^(2/3) z^(1/3)]))

Standard Form

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MathML Form

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</cn> <apply> <times /> <cn type='integer'> 9935310 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1924230 </cn> <ci> z </ci> </apply> <cn type='integer'> -366520 </cn> </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]