I understand, thank you for suck a deep explanation…
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суббота, 17 декабря 2022 г., 17:33 +0300 от emanuel.charpent...@gmail.com
<emanuel.charpent...@gmail.com>:
>Let’s dissecate this :
>>>> from sympy import symbols, fourier_series
>>>> t=symbols("t", real=True)
>>>> T=symbols("T", positive=True)
>>>> foo=fourier_series(1/t, (t, -T/2, T/2)) ; foo
>FourierSeries(1/t, (t, -T/2, T/2), (0, SeqFormula(0, (_k, 1, oo)),
>SeqFormula(4*sin(2*_n*pi*t/T)*Si(_n*pi)/T, (_n, 1, oo))))
>
>The constant term tof this series is taken to be 0. The even terms are all 0.
>The coefficient of the nth odd term is Si(n*pi). These coefficients do not
>converge to 0 :
>>>> k=symbols("k", integer=True)
>>>> limit(Si(k*pi), k, oo)
>pi/2
>
>therefore their sum does not necessarily converge.
>Therefore, the expressions returned by fourier_transform are analitically
>correct, but their existence do not imply their convergence.
>In other word, fourier series return the elements allowing computation of the
>Fourier series of the function if such a series exist , but do not assess
>its existence.
>HTH,
>
>Le mercredi 14 décembre 2022 à 19:15:24 UTC+1, antonv...@gmail.com a écrit :
>>Hi, I'm trying to find fourier series decomposition of 1/x function on [-3;
>>3] interval. IMHO, such a decomposition doesn't exist, because the a0 и an
>>doesn't exist (corresponding integrals doesn't converge). But sympy function
>>fourier_series, returns the answer (omitting the a0, an coefficients and only
>>taking into account the bn coefficients). Is there an error in fourier_series
>>function?
>>fourier_series(1/x,(x,-3,3)) =
>>(2/3)*sin(pi*x/3)*Si(pi)+(2/3)*sin(2*pi*x/3)*Si(2*pi)+(2/3)*sin(pi*x)*Si(3*pi)+...
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