The Mahler polynomials are presented in Mathworld, Wikipedia, and the OEIS (A08299). There are rich connections to several areas of analysis and statistical physics, including the Whitehouse simplicial complexes, phylogenetic trees, tropical Grassmannians, and the combinatorics of Lagrange inversion through OEIS A134991 and A134685, so I'm curious how Kurt Mahler used them in his 1930 monograph "Über die Nullstellen der unvollständigen Gammafunktionen.", Rendiconti Palermo (in German), 54: 1–41, on the zeros of the upper incomplete gamma function (the Cinderella function of Tricomi, which has rich links in calculus and operator theory). (I have no access to Mahler's monograph.)
Can someone sketch the use of these polynomials in Mahler's monograph?