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Fourier Cosine Series and Fourier Series Expansion

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.