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

Author

Iaroslav V. Blagouchine, Mar 11 2018

Keywords

• nonn
• cons

Comments

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

Examples

			0.3694861820952043731200546914239769936602361586790838...
		

Links

• 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.

Crossrefs

Cf. A195055, A300690, A300713, A300727.

Programs

MATLAB

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

Maple

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

Mathematica

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

PARI

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

Formula

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