Hermite-Padé polynomials associated with certain generalized hypergeometric functions (Q1263763)

Continuing his previous study [ibid. 42, 299-386 (1984; Zbl 0565.41015)], the author constructs two types of Hermite-Padé polynomials associated with the functions \(1,_ pF_{p-1}\left( \begin{matrix} a\\ c\end{matrix} ;x\right)\) and p-1 additional functions contiguous with this generalized hypergeometric function. The author uses some properties of Riemann modules and other techniques due to G. V. Chudnovsky and introduced the so-called augmented modules. The results of the paper under review might lead to the determination of the asymptotic behaviour of the Hermite- Padé polynomials and to shed some light on the author's earlier conjectures on this subject.