A300713 -id:A300713 - cp's OEIS frontend

A300690 Decimal expansion of sqrt(Pi^2/8 - 1).

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

Offset: 0

Iaroslav V. Blagouchine, Mar 11 2018

Also the total harmonic distortion (THD) of a square wave, see formula (11) in the Blagouchine & Moreau link.

			0.4834258476086790990137326370639317022328017276651459...

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.
Index entries for transcendental numbers

Cf. A002388, A111003, A300713, A300714, A300727, A300731.

MATLAB
```
format long; sqrt(pi^2/8-1)
```
Maple
```
evalf(sqrt((1/8)*Pi^2-1), 120)
```

RealDigits[Sqrt[Pi^2/8 - 1], 10, 120][[1]]

default(realprecision, 120); sqrt(Pi^2/8-1)

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

Original entry on oeis.org

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

Iaroslav V. Blagouchine, Mar 11 2018

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

			0.3694861820952043731200546914239769936602361586790838...

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.

Cf. A195055, A300690, A300713, A300727.

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

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

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

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

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

A300727 Decimal expansion of the total harmonic distortion (THD) of the sawtooth signal filtered by a 2nd-order low-pass filter.

Original entry on oeis.org

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

Offset: 0

Iaroslav V. Blagouchine, Mar 11 2018

See formula (34) in Blagouchine & Moreau link.

			0.1811416137938290040802181055813016784438928351595635...

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.

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

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))

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)

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]]

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

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).

A300731 Decimal expansion of sqrt(Pi^4/96 - 1).

Original entry on oeis.org

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

Offset: 0

Iaroslav V. Blagouchine, Mar 11 2018

Also the total harmonic distortion (THD) of a triangle wave, see formula (14) in the Blagouchine & Moreau link.

			0.1211529265193047433149738747453528509885975440568532...

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.
Index entries for transcendental numbers

Cf. A092425, A300690, A300707, A300713, A300714, A300727.

MATLAB
```
format long; sqrt(pi^4/96-1)
```
Maple
```
evalf(sqrt((1/96)*Pi^4-1), 120)
```

RealDigits[Sqrt[Pi^4/96 - 1], 10, 120][[1]]

default(realprecision, 120); sqrt(Pi^4/96-1)

cp's OEIS Frontend

A300690 Decimal expansion of sqrt(Pi^2/8 - 1).

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

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MATLAB

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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.

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MATLAB

Maple

Mathematica

PARI

Formula

A300731 Decimal expansion of sqrt(Pi^4/96 - 1).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

MATLAB

Maple

Mathematica

PARI