Are there situations in which the [polygamma](https://en.wikipedia.org/wiki/Polygamma_function) pops up naturally in a mathematical physics context? In particular: are there examples of potentials having some interest for which the dependence on the distance is expressed in terms of $\psi^{(n)}$?


**Update**: While Carlo Beenakker's answer is clearly useful, the references therein still don't contain exactly what I'm looking for in the second part of the question.



Polygamma function in mathematical physics
Abou-Salem, L. I., *A study on baryons spectroscopy using digamma-function as interacting potential*, <https://arxiv.org/abs/1311.6743> studies using the digamma function as an interaction potential (for quarks in baryons).


