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Use the pointwise convergence theorem to find the pointwise sum function of the series on R. Sketch its graph. Show that E =5. (This is the Basel problem, which was famously first solved by Euler long before Fourier methods were de- veloped) n2 6 Show that E=1 (-1)"+1 n2 12

Use the pointwise convergence theorem to find the pointwise sum function of the series on R. Sketch its graph. Show that E =5. (This is the Basel problem, which was famously first solved by Euler long before Fourier methods were de- veloped) n2 6 Show that E=1 (-1)"+1 n2 12

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. (a) Show that the Fourier series for f(x) = x², –n < x < T, is 42(-1)n-1 Cos(nx) n2 n=1 (b) Use the pointwise convergence theorem to find the pointwise sum function of the series on R. Sketch its graph. 1 Show that 7 =5. (This is the Basel problem, which was famously first solved by Euler long before Fourier methods were de veloped) Show that En=1 (-1)n+1 n2 12
Transcribed Image Text:3. (a) Show that the Fourier series for f(x) = x², –n < x < T, is 42(-1)n-1 Cos(nx) n2 n=1 (b) Use the pointwise convergence theorem to find the pointwise sum function of the series on R. Sketch its graph. 1 Show that 7 =5. (This is the Basel problem, which was famously first solved by Euler long before Fourier methods were de veloped) Show that En=1 (-1)n+1 n2 12
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