In the interval (-pi, pi), δn(x) = (n/x^1/2) e ^(-n^2 x^2)
a) Expand δn(x) as a Fourier Cosine Series.
b) Show that your Fourier Series agrees with a Fourier expansion of δn(x) in the limit as n--> infinity.
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I am including a short overview of Fourier series you can pretty much read past if you have seen it before. I found that expanding the exp(x^2) function in a Maclauren power series seemed to be the most profitable in obtaining values for the definite integrals. The values in the powers of m for the series expansion have ...
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Fourier Cosine Series and Fourier Series Expansion are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.
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Fourier Series Expansion: Example Problem
Please see the attached file for the fully formatted problems.
See f(x) in the file.
1. Sketch f(x) over -3<x<3
2. Is f(x) odd, even or neither?
3. Solve for the Fourier coefficients.
4. Write out the Fourier series expansion up to n=3
... the Fourier coefficients of the series expansion of f(x). ... The fourier coefficients of a function on the ... L 1 an f x cos dx L ...
Fourier Series Expansion. ... The general Fourier coefficients for a function over the interval [-L,L ... is an odd function over the interval as well (the cosine is an ...
... The general expansion of a function over the symmetric ... by: (1.3) Where: (1.4) Since the cosine function is ... if we want to expand into a Fourier series, we need ...
... 11. Using only your conclusions from problem 10, find the finite Fourier-Legendre series of f(x) = x2 If ... Then: ( ) 1 P2 (cos θ ) = 3 cos 2 θ − 1 2. ...
... (ii) Even function so only Cosine terms in the Fourier series expansion. ... (ii) Even symmetry so Cosine components only in Fourier series expansion. ...
... the function in a sine-cosine series and Computer ... resulting expansion will be the Fourier expansion of f(x ... Therefore the cosine Fourier coefficients will be zero ...
... of the sum 14 (ie plot x(t) = a0 + ∑ an cos(nΩ0t) + bn ... coefficients if you had instead calculated the complex exponential Fourier series expansion ∞ x(t ...
... But we are also given the expansion: ... a 1 1 b1 3 a2 0.5 b2 0 a3 0 b3 5 The general fourier series is given by ... a0 f (x ) = an cos (n wx ...
... in the interval, its Fourier series expansion will not ... functions is odd The fourier series representation of ... sin nx bn cos nx 2 n ...
... we cannot apply the standard Fourier series formulae on ... equation (3). Indeed, the standard Fourier expansion on interval ... b contains sines and cosines of forms ...
