A300714 - OEIS

%I #23 Mar 25 2018 14:59:58

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

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

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

%N Decimal expansion of the total harmonic distortion (THD) of the sawtooth signal filtered by a 1st-order low-pass filter.

%C See formula (33) 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>.

%F Equals sqrt(Pi^2/3 - Pi*coth(Pi)).

%e 0.3694861820952043731200546914239769936602361586790838...

%p evalf(sqrt((1/3)*Pi^2-Pi*coth(Pi)), 120)

%t RealDigits[Sqrt[Pi^2/3 - Pi*Coth[Pi]], 10, 120][[1]]

%o (PARI) default(realprecision, 120); sqrt(Pi^2/3-Pi/tanh(Pi))

%o (MATLAB) format long; sqrt(pi^2/3-pi*coth(pi))

%Y Cf. A195055, A300690, A300713, A300727.

%K nonn,cons

%O 0,1

%A _Iaroslav V. Blagouchine_, Mar 11 2018