I have come across the series:
$\sum_{j=1}^\infty \frac{x^j (j-1)}{j! \sqrt{2j - 1}}$
which is easily seen to be absolutely convergent everywhere (e.g. ratio test). It seems that it should be very close to $\exp(x)$ and I would like to characterize it exactly in terms of simple functions if possible. Does anyone have ideas?
Cheers.