Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.0719)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a=-11/2, b>=a

For fixed z and a=-11/2, b=-11/2

http://functions.wolfram.com/07.23.03.0719.01

Input Form

Hypergeometric2F1[-(11/2), -(11/2), 11/2, -z] == -((1/(343597383680 z^(9/2))) (3 (Sqrt[z] Sqrt[1 + z] (88935 + 2 z (1240855 + 32 z (617463 + z (8739346 + z (-1571226457 + 2 z (3682667235 + 16 z (-302888815 + 6 z (22242609 - 3018882 z + 82364 z^2)))))))) - 1155 (77 + 8 z (275 + z (4455 + 64 z (990 + z (24255 + 8 z (-43659 + z (121275 + 8 z (-13860 + z (4455 + 8 (-55 + z) z))))))))) ArcSinh[Sqrt[z]])))

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]