A243596 -id:A243596 - cp's OEIS frontend

A243597 Decimal expansion of the fraction of the full solid angle subtended by a cone with the polar angle of 1 radian.

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

Offset: 0

Stanislav Sykora, Jun 07 2014

Given a right circular cone with polar angle theta, the fraction of the full solid angle it subtends is (1-cos(theta))/2.

			0.22984884706593014129953169627851169813384478969103888616...

Stanislav Sykora, Table of n, a(n) for n = 0..2000
Wikipedia, Solid angle
Wikipedia, Cone

Cf. A243596 (solid angle).

RealDigits[(1-Cos[1])/2,10,120][[1]] (* Harvey P. Dale, Apr 14 2019 *)

PARI
```
(1-cos(1))/2
```

Equals (1-cos(1))/2.

Equals A243596/(4*Pi).

A371935 Decimal expansion of Sum_{k>=0} (-1)^k / ((k+1)(2k+1)!).

Original entry on oeis.org

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

Offset: 0

Clark Kimberling, Apr 24 2024

			0.91939538826372056519812678511404679253...

Cf. A049470, A243596, A272795, A371936.

s = N[Sum[(-1)^k/((k + 1) (2 k + 1)!), {k, 0, Infinity}], 120]
First[RealDigits[s]]

2*(1 - cos(1)) \\ Stefano Spezia, Apr 21 2025

Equals 2*(1 - cos(1)) = 2 * A371936.
From Hugo Pfoertner, Apr 26 2024: (Start)
Equals A243596/Pi.
Equals A272795^2. (End)

cp's OEIS Frontend

A243597 Decimal expansion of the fraction of the full solid angle subtended by a cone with the polar angle of 1 radian.

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A371935 Decimal expansion of Sum_{k>=0} (-1)^k / ((k+1)(2k+1)!).

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cp's OEIS Frontend

A243597 Decimal expansion of the fraction of the full solid angle subtended by a cone with the polar angle of 1 radian.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A371935 Decimal expansion of Sum_{k>=0} (-1)^k / ((k+1)*(2*k+1)!).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

A371935 Decimal expansion of Sum_{k>=0} (-1)^k / ((k+1)(2k+1)!).