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Tr. Mat. Inst. Steklova, 2018, Volume 301, Pages 241–258 (Mi tm3915)  

Hermite–Padé approximants of the Mittag-Leffler functions

A. P. Starovoitov

Francisk Skorina Gomel State University, Savetskaya vul. 104, Gomel, 246019 Belarus

Abstract: The convergence rate of type II Hermite–Padé approximants for a system of degenerate hypergeometric functions $\{_1F_1(1,\gamma;\lambda_jz)\}_{j=1}^k$ is found in the case when the numbers $\{\lambda_j\}_{j=1}^k$ are the roots of the equation $\lambda^k=1$ or real numbers and $\gamma\in\mathbb C\setminus\{0,-1,-2,…\}$. More general statements are obtained for approximants of this type (including nondiagonal ones) in the case of $k=2$. The theorems proved in the paper complement and generalize the results obtained earlier by other authors.

Funding Agency Grant Number
Ministry of Education of the Republic of Belarus
This work was supported by the Ministry of Education of the Republic of Belarus within the state program of scientific research for 2016–2020.


DOI: https://doi.org/10.1134/S0371968518020188

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English version:
Proceedings of the Steklov Institute of Mathematics, 2018, 301, 228–244

Bibliographic databases:

UDC: 517.538.5+517.518.84
Received: January 5, 2018

Citation: A. P. Starovoitov, “Hermite–Padé approximants of the Mittag-Leffler functions”, Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, MAIK Nauka/Interperiodica, Moscow, 2018, 241–258; Proc. Steklov Inst. Math., 301 (2018), 228–244

Citation in format AMSBIB
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\vol 301
\pages 241--258
\publ MAIK Nauka/Interperiodica
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  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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