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PFMT, 2017, Issue 1(30), Pages 73–77 (Mi pfmt491)  

MATHEMATICS

Asymptotics of the type II Hermite–Padé approximation of exponential functions with complex multipliers in the exponent

M. V. Sidortsov, N. A. Starovoitova, A. P. Starovoitov

F. Sсorina Gomel State University

Abstract: The asymptotic behavior of diagonal Hermite–Padé polynomials and diagonal Hermite–Padé approximations of type II for the system of exponentials $\{e^{\lambda_pz}\}_{p=0}^k$ in which $\lambda_0=0$, while the rest $\lambda_p$ are the roots of the equation $\xi^k=1$ is determined. The theorems complement known results of H. Padé, D. Braess, A. I. Aptekarev, H. Stahl, F. Wielonsky, W. Van Assche, A. B. J. Kuijlaars, A. P. Starovoitov, obtained for the case, where the $\{\lambda_p\}_{p=0}^k$ — different real numbers.

Keywords: Hermite integrals, Hermite–Padé polynomials, Hermite–Padé approximations, asymptotic equality.

Full text: PDF file (332 kB)
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UDC: 517.538.52+517.538.53
Received: 01.12.2016

Citation: M. V. Sidortsov, N. A. Starovoitova, A. P. Starovoitov, “Asymptotics of the type II Hermite–Padé approximation of exponential functions with complex multipliers in the exponent”, PFMT, 2017, no. 1(30), 73–77

Citation in format AMSBIB
\Bibitem{SidStaSta17}
\by M.~V.~Sidortsov, N.~A.~Starovoitova, A.~P.~Starovoitov
\paper Asymptotics of the type II Hermite--Pad\'e approximation of exponential functions with complex multipliers in the exponent
\jour PFMT
\yr 2017
\issue 1(30)
\pages 73--77
\mathnet{http://mi.mathnet.ru/pfmt491}


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