Prove that the following function is $C^\infty$ in the point $\xi=0$:
$$f:\Bbb R\to\Bbb C:\xi\mapsto {e^{i\cdot\xi\cdot λ}-1\over i\cdot\xi}-λ$$ Any way how to prove this? i think that i must use series but i do not know how
2026-04-13 04:41:40.1776055300
Prove that the following function is $C^\infty$ in the point $\xi=0$
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Hint. Use taylor's integral formula for $\xi \to e^{i\xi \lambda}$, then try to use some "regularity under the integral sign" theorem. Conclude by recurrence.