An explanation of Mellin's 1921 paper

In 1921 Mellin published a Comptes Rendu paper computing the principal solution of a polynomial using generalized hypergeometric functions of its coefficients. He used an integral transform nowadays bearing his name. Slightly over three pages, the paper is written in French in a terse style befitting the language. This article makes Mellin's landmark result accessible to people who are not experts in hypergeometric functions and complex analysis by deriving detailed proofs that were omitted in Mellin's paper.