A049471 -id:A049471 - cp's OEIS frontend

A346839 Decimal expansion of Sum_{n>=0} A346838(n) / n!.

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

Offset: 0

Peter Luschny, Aug 13 2021

			0.29340799302602338740477843394029002038314588271248926...

Cf. A049471, A073448, A346838.

A := n -> I*(polylog(-n, -I) - exp(I*Pi*n)*polylog(-n, I)) / exp(I*Pi*n/2):
Digits := 120; sum(A(n)/n!, n = 0..infinity): evalf(%)*10^91:
ListTools:-Reverse(convert(floor(%), base, 10));

RealDigits[Sec[1] - Tan[1], 10 , 100][[1]] (* Amiram Eldar, Aug 17 2021 *)

Equals sec(1) - tan(1) = A073448 - A049471. - Amiram Eldar, Aug 17 2021

A327555 Decimal expansion of number with continued fraction expansion [1; 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, ...].

Original entry on oeis.org

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

Offset: 1

Steven Ricardo Villeda Marroquín, Sep 16 2019

The continued fraction with even numbers and 1 alternated in opposition to A049471, that is, tan(1): [1; 1, 1, 3, 1, 5, 1, 7, 1, 9, 1, ...].

			1.353389234117675841935...

Cf. A049471, A093178.

N[FromContinuedFraction[Flatten[Table[{1, 2*k}, {k, 1, 100}]]], 100] (* Vaclav Kotesovec, Nov 08 2019 *)

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

Original entry on oeis.org

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

Bernard Schott, Jan 21 2022

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

			1.915315108720571527500554820864094552856972658463348659...

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

Cf. A049471, A073449.

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

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

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

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

A384932 Decimal expansion of tan(1) + sec(1).

Original entry on oeis.org

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

Offset: 1

Kritsada Moomuang, Jun 12 2025

The continued fraction expansion of this constant - 1 is A133265.

			3.408223442335827848481...

Cf. A049471, A073448, A133265, A248617.

RealDigits[Tan[1] + Sec[1], 10, 100, 0][[1]]

tan(1) + 1/cos(1) \\ Amiram Eldar, Jun 13 2025

Equals A049471 + A073448.
Equals 4 + Integral_{x=0..1} sin(x)/(sin(x) - 1) dx.
Equals exp(Integral_{x=0..1} sec(x) dx).
Equals exp(A248617). - Hugo Pfoertner, Jun 13 2025

cp's OEIS Frontend

A346839 Decimal expansion of Sum_{n>=0} A346838(n) / n!.

Views

Author

Keywords

Examples

Crossrefs

Programs

Maple

Mathematica

Formula

A327555 Decimal expansion of number with continued fraction expansion [1; 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, ...].

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Examples

References

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A384932 Decimal expansion of tan(1) + sec(1).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Formula