A350885 Decimal expansion of 1 - 2*cotan(2).

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

Offset: 1

Author

Bernard Schott, Jan 21 2022

Keywords

• nonn
• cons

Comments

The constant given in the name is computed using a telescopic sum coming from cotan(x) - 2*cotan(2*x) = tan(x).

Examples

			1.915315108720571527500554820864094552856972658463348659...
		

References

• J. Quinet, Cours élémentaire de Mathématiques Supérieures, Tome 3, Calcul intégral et Séries, Bordas, 1973, Exercice 7.36, pp 111 and 231.

Crossrefs

Cf. A049471, A073449.

Programs

Maple

evalf(1-2/tan(2),120);

Mathematica

RealDigits[1 - 2*Cot[2], 10, 100][[1]] (* Amiram Eldar, Jan 21 2022 *)

PARI

1-2*cotan(2) \\ Michel Marcus, Jan 21 2022

Formula

Equals Sum_{m>=0} (1/2^m) * (tan(1/2^m)).

Equals (t^2+t-1)/t with t=A049471. - Michel Marcus, Jan 21 2022