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Jul 5, 2019 at 9:09 comment added jarhead please refer again to my question
Jul 4, 2019 at 17:46 comment added Carlo Beenakker I'm not quite sure what you mean; the series $\sum_{n=1}^\infty n^{n-1}\frac{1}{n!}(rye^y)^n$ is a contiuous function of $y$; if you are asking whether the series can be summed in closed form, the answer is "yes", but that would bring you back to the Lambert W-function, which you wish to avoid.
Jul 4, 2019 at 16:54 comment added jarhead and can you transform this series to obtain a continuous function of $f(x)$ when $y=f(x)$?
Jul 4, 2019 at 13:22 history edited Carlo Beenakker CC BY-SA 4.0
added 22 characters in body
Jul 4, 2019 at 13:04 history answered Carlo Beenakker CC BY-SA 4.0