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On $\sum_{k=1}^\infty1/(k!k^s)$.
Has the following $\zeta$-like function been studied before?
$$f(z;s)=\sum_{k=1}^\infty\frac{z^k}{k!k^s}.$$
I believe this is an entire function since using the ratio test,
$$\lim_{n\to\infty}\frac{...
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