A254604 Decimal expansion of the half of a single half-wave constant.

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

Offset

0,1

Comments

By the definition this constant takes the value 0 < x < Pi such that the horizontal line y = sin x divides the region bounded by the sine curve and the interval [0,Pi] on the x-axis into two shapes of equal area.

Links

Table of n, a(n) for n=0..120.

Formula

2*cos(x) - (Pi - 2*x)*sin(x) = 1, 0 < x < Pi.

Example

x = 0.368305390596661399946991689932336338080760158209792727276899496553...

Mathematica

FindRoot[2 Cos[x] - (Pi - 2 x) Sin[x] - 1 == 0, {x, 0, Pi}, WorkingPrecision -> 150] (* Bruno Berselli, Feb 03 2015 *)

Prog

(PARI) solve(x=0, Pi, 2*cos(x) - (Pi - 2*x)*sin(x) - 1) \\ Michel Marcus, Feb 03 2015

Crossrefs

Sequence in context: A157032 A295655 A339621 * A278498 A011334 A200340

Adjacent sequences: A254601 A254602 A254603 * A254605 A254606 A254607

Keyword

nonn,cons

Author

Roman Witula, Feb 02 2015

Status

approved