Convergence of <munder> &#x2211;<!-- ∑ --> <mrow class="MJX-TeXAtom-ORD"> k

reryfaikear

reryfaikear

Answered question

2022-05-21

Convergence of k 1 e t k cos k z

Answer & Explanation

Travis Fernandez

Travis Fernandez

Beginner2022-05-22Added 10 answers

Note that cos k z = R e ( cos k z + i sin k z ) = R e ( e i k z ). Thus:
k 1 e t k cos k z = k 1 R e ( e t k ) R e ( e i k z ) = k 1 R e ( e k ( t + i z ) ) = R e ( k 1 ( e t + i z ) k )
which is a geometric series

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