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

The asymptotics of diagonal Hermite–Padé polynomials of the first kind is studied for the system of exponential functions { e λ p z } p = 0 k , where λ 0 = 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, Wi...

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Bibliographic Details
Published in:Mathematical Notes 2017-07, Vol.102 (1-2), p.277-288
Main Author: Starovoitov, A. P.
Format: Article
Language:English
Subjects:
Exponential functions
Functions (mathematics)
Hermite polynomials
Mathematical analysis
Mathematics
Mathematics and Statistics
Real numbers
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Summary:The asymptotics of diagonal Hermite–Padé polynomials of the first kind is studied for the system of exponential functions { e λ p z } p = 0 k , where λ 0 = 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.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S000143461707029X