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Mar 8, 2023 at 0:43 comment added Jan Bohr I agree that the two definitions are identical.
Mar 7, 2023 at 23:47 vote accept Peg Leg Jonathan
Mar 7, 2023 at 23:43 comment added Peg Leg Jonathan Thanks for your answer but i have question: if we define rapidly decreasing as for each $N \in \mathbb{N}$, there is $d_N > 0$ such that for all $k \neq 0$ we have $|c_k| \leq \frac{d_N}{|k|^{N}}$, we answer is the same right? I mean these two definitions are the same thing?
Mar 7, 2023 at 23:38 history answered Jan Bohr CC BY-SA 4.0