cp's OEIS Frontend

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

%I A300710 #27 Aug 21 2025 16:52:43
%S A300710 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,
%T A300710 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,
%U A300710 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
%N A300710 Decimal expansion of 17*Pi^8/161280.
%C A300710 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).
%H A300710 Jason Bard, <a href="/A300710/b300710.txt">Table of n, a(n) for n = 1..10000</a>
%H A300710 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%H A300710 Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See p. 21.
%F A300710 Equals 17*A092736/161280. - _Omar E. Pol_, Mar 11 2018
%F A300710 From _Artur Jasinski_, Jun 24 2025: (Start)
%F A300710 Equals DirichletL(2,1,8).
%F A300710 Equals DirichletL(4,1,8).
%F A300710 Equals DirichletL(8,1,8).
%F A300710 Equals DirichletL(16,1,8). (End)
%F A300710 Equals 255*Zeta(8)/256. - _Jason Bard_, Aug 21 2025
%e A300710 1.0001551790252961193029872492957280415665429750613740...
%p A300710 evalf((17/161280)*Pi^8, 120);
%t A300710 RealDigits[(17/161280)*Pi^8, 10, 120][[1]]
%o A300710 (PARI) default(realprecision, 120); (17/161280)*Pi^8
%o A300710 (MATLAB) format long; (17/161280)*pi^8
%Y A300710 Cf. A092736, A111003, A300707, A300709.
%K A300710 nonn,cons,changed
%O A300710 1,6
%A A300710 _Iaroslav V. Blagouchine_, Mar 11 2018