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A300727 Decimal expansion of the total harmonic distortion (THD) of the sawtooth signal filtered by a 2nd-order low-pass filter. 4
1, 8, 1, 1, 4, 1, 6, 1, 3, 7, 9, 3, 8, 2, 9, 0, 0, 4, 0, 8, 0, 2, 1, 8, 1, 0, 5, 5, 8, 1, 3, 0, 1, 6, 7, 8, 4, 4, 3, 8, 9, 2, 8, 3, 5, 1, 5, 9, 5, 6, 3, 5, 3, 8, 9, 1, 1, 5, 5, 6, 0, 6, 0, 8, 6, 2, 6, 4, 1, 4, 1, 9, 5, 6, 3, 6, 7, 9, 2, 4, 7, 3, 1, 6, 9, 8, 0, 7, 9, 1, 7, 9, 2, 7, 4, 4, 1, 6, 2, 1, 2, 2, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See formula (34) in 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*(cot(Pi/sqrt(2))*coth(Pi/sqrt(2))^2-cot(Pi/sqrt(2))^2*coth(Pi/sqrt(2))-cot(Pi/sqrt(2))-coth(Pi/sqrt(2)))/((cot(Pi/sqrt(2))^2+coth(Pi/sqrt(2))^2)*sqrt(2))+(1/3)*Pi^2-1).

EXAMPLE

0.1811416137938290040802181055813016784438928351595635...

MAPLE

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

MATHEMATICA

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

PROG

(MATLAB) format long; sqrt(sqrt(pi*(cot(pi/sqrt(2))*coth(pi/sqrt(2))^2-cot(pi/sqrt(2))^2*coth(pi/sqrt(2))-cot(pi/sqrt(2))-coth(pi/sqrt(2)))/((cot(pi/sqrt(2))^2+coth(pi/sqrt(2))^2)*sqrt(2))+(1/3)*pi^2-1))

(PARI) s2=sqrt(2);

A=Pi/s2;

B=1+2/(exp(2*A)-1)

C=1/tan(A);

sqrt(Pi*(B^2*C-B*C^2-C-B)/((C^2+B^2)*s2) + Pi^2/3 - 1) \\ Charles R Greathouse IV, Mar 11 2018

CROSSREFS

Cf. A247719 (Pi/sqrt(2)), A300690, A300713, A300714.

Sequence in context: A133421 A128881 A154015 * A246722 A197492 A153621

Adjacent sequences:  A300724 A300725 A300726 * A300728 A300729 A300730

KEYWORD

nonn,cons

AUTHOR

Iaroslav V. Blagouchine, Mar 11 2018

STATUS

approved

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Last modified February 17 02:22 EST 2020. Contains 331976 sequences. (Running on oeis4.)