Is there a slowly varying function $L(.)$ with given properties?

I am looking for a slowly varying function $L(.)$ such that the function $f(s)=s+(1-s)^2L\left( \frac{1}{1-s}\right)$ is a probability generating function with $f'(1)=1$ and $f''(1)=\infty$. I...

03 July 2022 6,123 1 View