Prove that if f(2) is an odd function, that is, f(-2) = –-f(2) for all z E C, and f is analytic in a open disk containing 0, then the power series of f at z0 O contains only odd terms.
Prove that if f(2) is an odd function, that is, f(-2) = –-f(2) for all z E C, and f is analytic in a open disk containing 0, then the power series of f at z0 O contains only odd terms.
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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Transcribed Image Text:Prove that if f(2) is an odd function, that is, f(-2) = –-f(2) for all z E C, and f is analytic in a open disk
containing 0, then the power series of f at z0
O contains only odd terms.
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