Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.5148)

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/07.23.03.5148.01

Input Form

Hypergeometric2F1[-(14/3), -(10/3), 11/2, -z] == (6561 (Sqrt[z] (-74317824 - 1550843904 z - 17543856128 z^2 - 163882729472 z^3 + 13210329289443 z^4 - 17643776769121 z^5 - 14881992629308 z^6 + 14376023303976 z^7 - 1741108692320 z^8 + 2796832384 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (222953472 + 4586471424 z + 51301974016 z^2 + 477034184704 z^3 + 7093534457856 z^4 - 60816777501601 z^5 + 85713178993364 z^6 - 31429049823960 z^7 + 2459894615008 z^8 + 2796832384 z^9) Sinh[ArcSinh[Sqrt[z]]/3]))/ (102481630431415235 z^(9/2) 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]