Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab07)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-17/4, b>=a

For fixed z and a=-17/4, b=6

http://functions.wolfram.com/07.23.03.ab07.01

Input Form

Hypergeometric2F1[-(17/4), 6, 15/4, z] == (1/(4294967296 z^(11/4))) (11 (2 z^(3/4) (-13923 - 186966 z + 192067435 z^2 - 1221211796 z^3 + 2685902947 z^4 - 2478321846 z^5 + 821665845 z^6) + 13923 (-1 + z)^2 (-3 - 45 z - 750 z^2 + 21750 z^3 - 71775 z^4 + 59015 z^5) ArcTan[z^(1/4)] - 13923 (-1 + z)^2 (-3 - 45 z - 750 z^2 + 21750 z^3 - 71775 z^4 + 59015 z^5) ArcTanh[z^(1/4)]))

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]