Show that the series00fx)-Σ -" cos n'xin=0is infinitely differentiable everywhere, but the Taylor series about x = 0flM(0)Σn!n=0does not converge except for the origin.

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Answered: Show that the series 00 f)-Σε -" cos n…

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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Show that the series 00 f)-Σε -" cos n *x n=0 is infinitely differentiable everywhere, but the Taylor series about x = 0 f" (0) n! n=0 does not converge except for the origin.