A377405 Decimal expansion of Pi*csc(Pi/5).

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

Offset: 1

Author

Stefano Spezia, Oct 27 2024

Keywords

• nonn
• cons

Examples

			5.344796660577975567125921862534413199507254626...
		

References

• Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.5.4, p. 33.

Links

• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 360.
• Index entries for transcendental numbers.

Crossrefs

Cf. A000796, A001622, A002163, A010476, A019692, A175380, A345019, A340722, A352324.

Programs

Mathematica

RealDigits[Pi*Csc[Pi/5],10,100][[1]]

Formula

Equals Gamma(1/5)*Gamma(4/5) = 2*Pi*sqrt(5)*sqrt(2+phi)/5 (see Finch).

Equals Integral_{x=0..oo} log(1 + x^(-5)) dx (see Shamos).

Equals sqrt(2*(1 + 1/sqrt(5)))*Pi.

Equals 10 * Sum_{n>=1} (-1)^(n+1)/A345019(n). - Amiram Eldar, Oct 27 2024

Equals 5*A352324. - Hugo Pfoertner, Oct 28 2024