A300713 - OEIS

%I #14 Sep 30 2022 23:27:44

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

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

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

%N Decimal expansion of sqrt(Pi^2/6 - 1) = sqrt(zeta(2) - 1).

%C Also the total harmonic distortion (THD) of a sawtooth signal, see formula (15) 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>

%F Equals sqrt(A013661 - 1).

%e 0.8030778709740584281843212446690348231898910996409661...

%p evalf(sqrt((1/6)*Pi^2-1), 120)

%t RealDigits[Sqrt[Pi^2/6 - 1], 10, 120][[1]]

%o (PARI) default(realprecision, 120); sqrt(Pi^2/6-1)

%o (MATLAB) format long; sqrt(pi^2/6-1)

%Y Cf. A013661, A300690, A300714, A300727, A300731.

%K nonn,cons

%O 0,1

%A _Iaroslav V. Blagouchine_, Mar 11 2018