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Asymptotics of diagonal Hermite–Padé polynomials for the collection of exponential functions

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Abstract

The asymptotics of diagonal Hermite–Padé polynomials of the first kind is studied for the system of exponential functions \(\left\{ {{e^{{\lambda _p}z}}} \right\}_{p = 0}^k\), where λ0 = 0 and the other λ p are the roots of the equation ξ k = 1. The theorems proved in the paper supplement the well-known results due to Borwein, Wielonsky, Stahl, Astaf’eva, and Starovoitov obtained for the case in which {λ p } p=0 k are different real numbers.

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  1. Fransisk Skorina Gomel State University, Gomel, Belarus

    A. P. Starovoitov

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Original Russian Text © A. P. Starovoitov, 2017, published in Matematicheskie Zametki, 2017, Vol. 102, No. 2, pp. 302–315.

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Starovoitov, A.P. Asymptotics of diagonal Hermite–Padé polynomials for the collection of exponential functions. Math Notes 102, 277–288 (2017). https://doi.org/10.1134/S000143461707029X

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