A254615 Decimal expansion of the left Alzer's constant x.

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

Offset

1,3

Comments

The left Alzer's constant x is defined to be the best constant in the left Alzer's inequality: x*abs(sin(cos a) + sin(sin a)) <= abs(cos a + sin a), where a is any real number.

Links

Table of n, a(n) for n=1..100.

Horst Alzer, A trigonometric double-inequality, Elemente der Mathematik 65 (2010), 45-48.

Formula

x = (sqrt(2)*sin(1/sqrt(2)))^(-1).

x = Sum_{k=-oo..oo} (-1)^k/(1 - 2*(Pi*k)^2). - Bruno Berselli, Feb 03 2015

Example

x = 1.088464554044397392026605399544901779407224058765958312439431735...

Mathematica

RealDigits[(Sqrt[2] Sin[1/Sqrt[2]])^(-1), 10, 100][[1]] (* Bruno Berselli, Feb 03 2015 *)

Prog

(PARI) 1/(sqrt(2)*sin(1/sqrt(2))) \\ Michel Marcus, Feb 03 2015

Crossrefs

Sequence in context: A154845 A370971 A126600 * A154841 A258984 A112116

Adjacent sequences: A254612 A254613 A254614 * A254616 A254617 A254618

Keyword

nonn,cons

Author

Roman Witula, Feb 03 2015

Status

approved