A201504 -id:A201504 - cp's OEIS frontend

A334367 Decimal expansion of Sum_{k>=0} 1/(4*k+2)!!.

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

Offset: 0

Ilya Gutkovskiy, Apr 24 2020

This constant is transcendental.

			1/(2^1*1!) + 1/(2^3*3!) + 1/(2^5*5!) + ... = 0.52109530549374736162242...

Index entries for transcendental numbers

Cf. A019774, A067626, A073742, A143280, A160327, A201504, A334366.

Mathematica
```
RealDigits[Sinh[1/2], 10, 110] [[1]]
```
PARI
```
sinh(1/2) \\ Michel Marcus, Apr 25 2020
```

Equals sinh(1/2).

Equals (1/2) * Product_{k>=1} 1 + 1/(2*k*Pi)^2. - Amiram Eldar, Jul 16 2020

A201505 Decimal expansion of cos(1/2).

Original entry on oeis.org

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

Offset: 0

R. J. Mathar, Dec 02 2011

By the Lindemann-Weierstrass theorem, this constant is transcendental. - Charles R Greathouse IV, May 13 2019

			0.877582561890372716... = sqrt((1+A049470)/2) = sqrt(1-A201504^2).

Index entries for transcendental numbers

Cf. A053988.

Maple
```
evalf(cos(1/2)) ;
```

RealDigits[Cos[1/2],10,120][[1]] (* Harvey P. Dale, Sep 22 2016 *)

cos(1/2) \\ Charles R Greathouse IV, May 13 2019

Taylor series representation: 1 -1/(2^2*2!) +1/(2^4*4!) -1/(2^6*6!) -...

A272795 Decimal expansion of 2*sin(1/2).

Original entry on oeis.org

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

Offset: 0

Peter M. Chema, May 22 2016

The length of the line underlying an arc of one radian with radius 1 (i.e., the linear distance for ends of an arc length 1 having same length as radius).

			0.958851077208406000546575870431142776163606735881201350377...

Cf. A201504, A371935.

RealDigits[2 Sin[1/2], 10, 100][[1]] (* Ilya Gutkovskiy, May 22 2016 *)

2*sin(1/2) \\ Stefano Spezia, Apr 21 2025

Equals i*e^(-i/2) - i*e^(i/2).
Equals 2*A201504.
Equals Sum_{k>=0} 2*(-1)^k*(1/2 - Pi/2)^(2*k)/(2*k)!. - Ilya Gutkovskiy, May 22 2016
Equals sqrt(A371935). - Hugo Pfoertner, Apr 21 2025

More digits from Jon E. Schoenfield, Mar 15 2018

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A334367 Decimal expansion of Sum_{k>=0} 1/(4*k+2)!!.

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A201505 Decimal expansion of cos(1/2).

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A272795 Decimal expansion of 2*sin(1/2).

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