A275486 - OEIS

A275486

Decimal expansion of Pi_3, the analog of Pi for generalized trigonometric functions of order p=3.

2, 4, 1, 8, 3, 9, 9, 1, 5, 2, 3, 1, 2, 2, 9, 0, 4, 6, 7, 4, 5, 8, 7, 7, 1, 0, 1, 0, 1, 8, 9, 5, 4, 0, 9, 7, 6, 3, 7, 8, 7, 5, 4, 9, 9, 7, 4, 5, 6, 9, 8, 7, 4, 3, 4, 0, 9, 3, 1, 7, 9, 9, 1, 3, 8, 5, 0, 8, 3, 0, 9, 0, 8, 1, 6, 8, 4, 7, 1, 8, 4, 4, 9, 1, 2, 1, 6, 6, 6, 5, 0, 9, 4, 9, 4, 1, 3, 5, 5, 8, 4, 7

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OFFSET

1,1

COMMENTS

The area of the circumcircle of a unit-area equilateral triangle. - Amiram Eldar, Aug 13 2020

LINKS

Table of n, a(n) for n=1..102.

David Edmunds and Jan Lang, Generalizing trigonometric functions from different points of view, 2009.

Shingo Takeuchi, A new form of the generalized complete elliptic integrals, arXiv:1411.4778 [math.CA], 2014.

FORMULA

Pi_3 = 2*Pi/(3*sin(Pi/3)) = 2/3 * gamma(1/3) * gamma(2/3) = 4*Pi/(3 * sqrt(3)).

Pi_3 = Sum_{n>=1} 4/(9*n^2 - 9*n + 2).