Hi,
Is there a way to recover the general formula for a fourier series? That is, f.fourier_series_sine_coefficient(9,pi) will give me the 9th sine coefficient, but I'd like to know more generally how I can construct the Nth sine coefficient.
I'm doing some complicated (to me) fourier series, and I'm having trouble figuring out the formula for the Nth.
Thanks for any help.
Andrew
Also:
sage: maxima('load(fourie)')
sage: maxima('foursimp(fourier(x^3,x,%pi))')
[%t26,%t27,%t28]
sage: maxima('[%t26,%t27,%t28]')
[a[0]=0,a[n]=0,b[n]=-2(%pi^2n^2-6)*(-1)^n/n^3]
I would recommend also the class notes by Prof. David Joyner:
In simple cases you can try:
sage: maxima('load(fourie)')
sage: maxima('totalfourier(abs(x),x,%pi)').sage()
1/2pi + 2sum(((-1)^n - 1)cos(nx)/n^2, n, 1, +Infinity)/pi
sage: maxima('totalfourier(x^3,x,%pi)').sage()
-2sum((pi^2n^2 - 6)(-1)^nsin(n*x)/n^3, n, 1, +Infinity)
Asked: 2011-12-29 15:52:24 +0100
Seen: 1,006 times
Last updated: Dec 30 '11
Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.
Can you explain what you mean by that? Generally the coefficients of the fourier series are not related to one another. One can write a expression for the nth coefficient only in special cases, and I am not sure there is a way of identifying whether a given formula falls in that category.
It may be a poor question then .. my frame of reference is the typical fourier series for periodic functions found on-line (square, triangle, saw), which all seem to reduce to nice clean equations for the nth coefficient. I didn't realize most would not behave so nicely .. though, I don't feel so bad now for scratching my head about the more complex function for which I was trying to generate a series .. smile. Thanks for the input/answer.