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edited title

edited May 30 at 21:47

The potato eater

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Does any such family of functions exist?

Is there a sequence of non-zero bounded smooth functions $f_1,f_2,\ldots,f_k$ so that

$$\sum_{I=1}^k \cos(f_i)= \cos\left(\sum_{i=1}^k f_i \right)$$

and what about the infinite case ?

sequences-and-series periodic-functions

asked May 30 at 21:45

The potato eater

49
7