Closed-form Expression for the Series $\sum_{n=0}^{\infty}{1 \over (kn)!}$

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2025年12月23日

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Jewel Mahajan

摘要

This article contains a closed-form expression for the infinite series $\sum_{n=0}^{\infty}{1 \over (kn)!}$ $\sum_{n = 0}^{\infty} \frac{1}{(k n)!}$ , where $k\in \mathbb{N}$ $k \in N$ . The solution is obtained using the series expression for exponential functions and roots of unity.

Closed-form Expression for the Series \(\sum_{n=0}^{\infty}{1 \over (kn)!}\)

摘要