A300714 Decimal expansion of the total harmonic distortion (THD) of the sawtooth signal filtered by a 1st-order low-pass filter.

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, 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, 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

Offset

0,1

Comments

See formula (33) in the Blagouchine & Moreau link.

Links

Table of n, a(n) for n=0..102.

I. V. Blagouchine and E. Moreau, Analytic Method for the Computation of the Total Harmonic Distortion by the Cauchy Method of Residues. IEEE Trans. Commun., vol. 59, no. 9, pp. 2478-2491, 2011. PDF file.

Formula

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

Example

0.3694861820952043731200546914239769936602361586790838...

Maple

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

Mathematica

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

Prog

(PARI) default(realprecision, 120); sqrt(Pi^2/3-Pi/tanh(Pi))
(MATLAB) format long; sqrt(pi^2/3-pi*coth(pi))

Crossrefs

Cf. A195055, A300690, A300713, A300727.

Sequence in context: A195771 A086276 A176322 * A020850 A163341 A197002

Adjacent sequences: A300711 A300712 A300713 * A300715 A300716 A300717

Keyword

nonn,cons

Author

Iaroslav V. Blagouchine, Mar 11 2018

Status

approved