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A254615 The decimal expansion of the left Alzer's constant x. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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.

REFERENCES

H. Alzer, A trigonometric double-inequality, Elemente der Mathematik 65 (2010), 45-48, doi: 10.4171/EM/139.

LINKS

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

FORMULA

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

x = Sum_{k=-infinity..infinity} (-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: A154012 A154845 A126600 * A154841 A258984 A112116

Adjacent sequences:  A254612 A254613 A254614 * A254616 A254617 A254618

KEYWORD

nonn,cons

AUTHOR

Roman Witula, Feb 03 2015

STATUS

approved

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Last modified May 28 17:28 EDT 2020. Contains 334684 sequences. (Running on oeis4.)