Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab0b)

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.ab0b.01

Input Form

Hypergeometric2F1[-(17/4), 6, 23/4, z] == (1/(1649267441664 z^(19/4))) (209 (2 z^(3/4) (-255255 - 875160 z - 2903940 z^2 - 12193896 z^3 + 3847775190 z^4 - 15602627880 z^5 + 23828533820 z^6 - 16166830680 z^7 + 4108329225 z^8) + 69615 (-1 + z)^4 (-11 - 77 z - 350 z^2 - 1450 z^3 - 7975 z^4 + 59015 z^5) ArcTan[z^(1/4)] - 69615 (-1 + z)^4 (-11 - 77 z - 350 z^2 - 1450 z^3 - 7975 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]