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

Author

Roman Witula, Feb 03 2015

Keywords

• nonn
• cons

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.

Examples

			x = 1.088464554044397392026605399544901779407224058765958312439431735...
		

Links

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

Programs

Mathematica

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

PARI

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

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