# Polygamma function in mathematical physics

Are there situations in which the polygamma 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.