Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5142)

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=-14/3, b>=a

For fixed z and a=-14/3, b=-10/3

http://functions.wolfram.com/07.23.03.5142.01

Input Form

Hypergeometric2F1[-(14/3), -(10/3), 5/2, -z] == (27 (Sqrt[z] (-917504 + 539880177 z - 2306967723 z^2 - 54290404 z^3 + 2283319704 z^4 - 508703904 z^5 + 1451392 z^6) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (2752512 + 164233216 z - 3438934267 z^2 + 9605221420 z^3 - 6119707112 z^4 + 759794720 z^5 + 1451392 z^6) Sinh[ArcSinh[Sqrt[z]]/3]))/ (16062203755 z^(3/2) Sqrt[1 + 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]