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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

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).

Pi_3 = 2*Integral_{0..1} (1-x^3)^(-1/3) dx.

Equals 1 + A263498.

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 A207605 A112931

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 September 16 12:57 EDT 2019. Contains 327113 sequences. (Running on oeis4.)