A300710 Decimal expansion of 17*Pi^8/161280.

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

Offset: 1

Author

Iaroslav V. Blagouchine, Mar 11 2018

Keywords

• nonn
• cons
• changed

Comments

Also the sum of the series Sum_{n>=0} (1/(2n+1)^8), whose value is obtained from zeta(8) given by L. Euler in 1735: Sum_{n>=0} (2n+1)^(-s)=(1-2^(-s))*zeta(s).

Examples

			1.0001551790252961193029872492957280415665429750613740...
		

Links

• Jason Bard, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers
• Michael I. Shamos, A catalog of the real numbers, (2007). See p. 21.

Crossrefs

Cf. A092736, A111003, A300707, A300709.

Programs

MATLAB

format long; (17/161280)*pi^8

Maple

evalf((17/161280)*Pi^8, 120);

Mathematica

RealDigits[(17/161280)*Pi^8, 10, 120][[1]]

PARI

default(realprecision, 120); (17/161280)*Pi^8

Formula

Equals 17*A092736/161280. - Omar E. Pol, Mar 11 2018

From Artur Jasinski, Jun 24 2025: (Start)

Equals DirichletL(2,1,8).

Equals DirichletL(4,1,8).

Equals DirichletL(8,1,8).

Equals DirichletL(16,1,8). (End)

Equals 255*Zeta(8)/256. - Jason Bard, Aug 21 2025