login
Decimal expansion of sqrt(Pi^4/96 - 1).
3

%I #11 Oct 01 2022 00:17:37

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

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

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

%N Decimal expansion of sqrt(Pi^4/96 - 1).

%C Also the total harmonic distortion (THD) of a triangle wave, see formula (14) in the Blagouchine & Moreau link.

%H I. V. Blagouchine and E. Moreau, <a href="http://dx.doi.org/10.1109/TCOMM.2011.061511.100749">Analytic Method for the Computation of the Total Harmonic Distortion by the Cauchy Method of Residues.</a> IEEE Trans. Commun., vol. 59, no. 9, pp. 2478-2491, 2011. <a href="http://iblagouchine.perso.centrale-marseille.fr/IEEE-TCOM-2011-061511-100749.php">PDF file</a>.

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

%e 0.1211529265193047433149738747453528509885975440568532...

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

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

%o (PARI) default(realprecision, 120); sqrt(Pi^4/96-1)

%o (MATLAB) format long; sqrt(pi^4/96-1)

%Y Cf. A092425, A300690, A300707, A300713, A300714, A300727.

%K nonn,cons

%O 0,2

%A _Iaroslav V. Blagouchine_, Mar 11 2018