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 A275486 Decimal expansion of Pi_3, the analog of Pi for generalized trigonometric functions of order p=3. 0
 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The area of the circumcircle of a unit-area equilateral triangle. - Amiram Eldar, Aug 13 2020 LINKS 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). Pi_3 = 2*Integral_{0..1} (1-x^3)^(-1/3) dx. Equals 1 + A263498. Equals Integral_{x=0..oo} 1/(1 + x^(3/2)) dx. - Amiram Eldar, Aug 13 2020 EXAMPLE 2.41839915231229046745877101018954097637875499745698743409317991385... MATHEMATICA RealDigits[4 Pi/(3 Sqrt[3]), 10, 102][[1]] PROG (PARI) 4*Pi/sqrt(27) \\ Charles R Greathouse IV, Aug 01 2016 CROSSREFS Sequence in context: A248112 A173122 A232723 * A065278 A182896 A207605 Adjacent sequences:  A275483 A275484 A275485 * A275487 A275488 A275489 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Jul 30 2016 STATUS approved

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Last modified July 25 19:34 EDT 2021. Contains 346291 sequences. (Running on oeis4.)