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5. Rederive the Maclaurin series for the function f(2) = cos z by (a) using the definition eiz +e-iz 2 cos z and appealing to the Maclaurin serles for e (b) showing that f(2m) (0) = (-1)" and f(2n+1)(0) = 0 (n = 0, 1,2, ...).

5. Rederive the Maclaurin series for the function f(2) = cos z by (a) using the definition eiz +e-iz 2 cos z and appealing to the Maclaurin serles for e (b) showing that f(2m) (0) = (-1)" and f(2n+1)(0) = 0 (n = 0, 1,2, ...).

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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5. Rederive the Maclaurin series for the function f(z) = cos z by (a) using the definition eit +e-iz cos z and appealing to the Maclaurin series for e (b) showing that flen (0) = (-1)" and f2n+1)(0) = 0 (n = 0, 1, 2, ...). 6. Use representation (2), Sec. 59, for sin z to write the Maclaurin series for the function f(2) = sin(2?). and point out how it follows that f(an) (0) = 0 and flen+)(0) = 0 (n = 0, 1, 2,...).
Transcribed Image Text:5. Rederive the Maclaurin series for the function f(z) = cos z by (a) using the definition eit +e-iz cos z and appealing to the Maclaurin series for e (b) showing that flen (0) = (-1)" and f2n+1)(0) = 0 (n = 0, 1, 2, ...). 6. Use representation (2), Sec. 59, for sin z to write the Maclaurin series for the function f(2) = sin(2?). and point out how it follows that f(an) (0) = 0 and flen+)(0) = 0 (n = 0, 1, 2,...).
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