3. Consider f (x) = e", 0< I < T. (a) Find the half-range Fourier sine and Fourier cosine expansions of f and com- pare their convergence at the endpoints r = 0 and = T

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 68E
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3. Consider f (x) = e", 0< I < T.
(a) Find the half-range Fourier sine and Fourier cosine expansions of f and com-
pare their convergence at the endpoints r = 0 and r = T
(b) Evaluate the obtained Fourier cosine series of f at the endpoints and deduce
the sum of the resultant infinte series.
Transcribed Image Text:3. Consider f (x) = e", 0< I < T. (a) Find the half-range Fourier sine and Fourier cosine expansions of f and com- pare their convergence at the endpoints r = 0 and r = T (b) Evaluate the obtained Fourier cosine series of f at the endpoints and deduce the sum of the resultant infinte series.
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