Could be tetration if this integral converges

[sheldonison]

What are the values for F (0,1,2,3)?

\( ^0 e \), \( ^1 e \), \( ^2 e \), \( ^3 e \), ... .

Very nice. I didn't have time to figure out why F is "an entire interpolant" for tetration until this morning. This version behaves a little better at the real axis.
\( F(z) = \sum_{n=0}^{\infty} e^{(^{n-1} e) (z - n + 1)} \frac{(-1)^n \sin(\pi z)}{\pi (z - n)} \)

- Sheldon