Geodesic
The convergence rate of Hermite--Pad\'e approximations of the three exponent system
Problemy fiziki, matematiki i tehniki, no. 1 (2020), pp. 81-84.

Voir la notice de l'article provenant de la source Math-Net.Ru

The convergence rate of type II Hermite–Padé approximants for the system $\{e^{\lambda_jz}\}_{j=1}^3$ is found. The theorems proved in the paper complement the results obtained earlier by O. Perron, D. Braess, A.I. Aptekarev, A.P. Starovoitov and other authors.
Keywords: type II Hermite–Padé approximations, system of exponential functions, asymptotic equalities, Hermite integrals. 
@article{PFMT_2020_1_a11,
     author = {E. P. Kechko},
     title = {The convergence rate of {Hermite--Pad\'e} approximations of the three exponent system},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {81--84},
     publisher = {mathdoc},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2020_1_a11/}
}
TY  - JOUR
AU  - E. P. Kechko
TI  - The convergence rate of Hermite--Pad\'e approximations of the three exponent system
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2020
SP  - 81
EP  - 84
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2020_1_a11/
LA  - ru
ID  - PFMT_2020_1_a11
ER  - 
%0 Journal Article
%A E. P. Kechko
%T The convergence rate of Hermite--Pad\'e approximations of the three exponent system
%J Problemy fiziki, matematiki i tehniki
%D 2020
%P 81-84
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2020_1_a11/
%G ru
%F PFMT_2020_1_a11
E. P. Kechko. The convergence rate of Hermite--Pad\'e approximations of the three exponent system. Problemy fiziki, matematiki i tehniki, no. 1 (2020), pp. 81-84. http://geodesic.mathdoc.fr/item/PFMT_2020_1_a11/

[1] C. Hermite, “Sur la fonction exponentielle”, C.R. Acad. Sci., 77 (1873), 18–24 ; 74–79 ; 226–233 ; 285–293 | Zbl

[2] E.M. Nikishin, V.N. Sorokin, Ratsionalnye approksimatsii i ortogonalnost, Nauka, M., 1988, 256 pp.

[3] Dzh. Beiker ml., P. Greivs-Morris, Approksimatsii Pade, v. 1, Osnovy teorii; т. 2, Обобщения и приложения, Мир, М., 1986, 502 с.

[4] O. Perron, Die Lehre von den Kettenbrüchen, Teubner, Leipzig, 1929, 524 pp. | MR | Zbl

[5] D. Braess, “On the conjecture of Meinardus on rational approximation of $e^z$, II”, J. Approx. Theory, 40:4 (1984), 375–379 | DOI | MR | Zbl

[6] A.I. Aptekarev, “O skhodimosti ratsionalnykh approksimatsii k naboru eksponent”, Vestn. MGU. Seriya 1. Matematika. Mekhanika, 1981, no. 1, 68–74

[7] A.B.J. Kuijlaars, H. Stahl, W. Van Assche, F. Wielonsky, “Type II Hermite–Padé approximation to the exponential function”, J. of Comput. and Appl. Math., 207:2 (2007), 227–244 | DOI | MR | Zbl

[8] A.P. Starovoitov, “Ermitovskaya approksimatsiya dvukh eksponent”, Izvestiya Saratovskogo universiteta. Novaya seriya. Seriya Matematika. Mekhanika. Informatika, 13:1-2 (2013), 88–91 | Zbl

[9] A.P. Starovoitov, “Approksimatsii Ermita–Pade funktsii Mittag-Lefflera”, Trudy MIAN, 301, 2018, 241–258 | DOI | Zbl

[10] E.P. Kechko, M.V. Sidortsov, “Asimptotika approksimatsii Ermita–Pade sistemy trekh eksponent”, Izvestiya Gomelskogo gosudarstvennogo universiteta imeni F. Skoriny, 2019, no. 3 (144), 158–162