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PFMT, 2018, Issue 1(34), Pages 71–78 (Mi pfmt557)  

MATHEMATICS

Speed of convergence of quadratic Hermite–Padé approximations confluent hypergeometric functions

M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov

F. Scorina Gomel State University

Abstract: The speed of convergence (including non-diagonal) of quadratic Hermite–Padé approximations of the system of the second kind $\{_1F_1(1,\gamma;\lambda_jz)\}^2_{j=1}$ is found. It consists of two degenerate hypergeometric functions when $\{\lambda_j\}_{j=1}^2$ are arbitrary distinct complex numbers, and $\gamma\in\mathbb{C}\setminus\{0, -1, -2,…\}$. These proved theorems supplement and generalize the results obtained earlier by other authors.

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

Full text: PDF file (373 kB)
References: PDF file   HTML file
UDC: 517.538.52+517.538.53
Received: 22.01.2018

Citation: M. V. Sidortsov, A. A. Drapeza, A. P. Starovoitov, “Speed of convergence of quadratic Hermite–Padé approximations confluent hypergeometric functions”, PFMT, 2018, no. 1(34), 71–78

Citation in format AMSBIB
\Bibitem{SidDraSta18}
\by M.~V.~Sidortsov, A.~A.~Drapeza, A.~P.~Starovoitov
\paper Speed of convergence of quadratic Hermite--Pad\'e approximations confluent hypergeometric functions
\jour PFMT
\yr 2018
\issue 1(34)
\pages 71--78
\mathnet{http://mi.mathnet.ru/pfmt557}


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