A300707 - OEIS

%I #21 Sep 28 2022 14:14:49

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

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

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

%N Decimal expansion of Pi^4/96.

%C Also the sum of the series Sum_{n>=0} (1/(2n+1)^4), whose value is obtained from zeta(4) given by L. Euler in 1735: Sum_{n>=0} (2n+1)^(-s) = (1-2^(-s))*zeta(s).

%C For the partial sums of this series see A120269/A128493. - _Wolfdieter Lang_, Sep 02 2019

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals A092425/96. - _Omar E. Pol_, Mar 11 2018

%F Equals (15/16)*zeta(4) = (15/16)*A013662. - _Wolfdieter Lang_, Sep 02 2019

%e 1.0146780316041920545462534655073449088513290174238064...

%p evalf((1/96)*Pi^4, 120)

%t RealDigits[Pi^4/96, 10, 120][[1]]

%o (PARI) default(realprecision, 120); Pi^4/96

%o (MATLAB) format long; pi^4/96

%Y Cf. A013662, A092425, A111003, A120269, A128493, A300709, A300710, A300731.

%K nonn,cons

%O 1,4

%A _Iaroslav V. Blagouchine_, Mar 11 2018