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PFMT, 2010, Issue 4(5), Pages 46–49 (Mi pfmt198)  

MATHEMATICS

Determinant representation of Pade joint approximations

A. P. Starovoitov, N. V. Rjabchenko

F. Skorina Gomel State University, Gomel

Abstract: Determinant formulas for numerators and denominators of joint approximations of Pade $\pi_j(z), j=1,2 …,r$ of perfect system of functions $\{f_j(z)\}^r_{j=1}$ are established. The analogue of the Pade theorem is proved and the obvious kind of the remainders is found at the approach $f_j(z)$ by the rational function $\pi_j(z)$ . The received theorems supplement and generalise the known results of Ermite, Pade, K. Mahler, E.M. Nikishin, A.I. Aptekarev and other authors.

Keywords: sedate a number, approximations of Pade, joint approximations of Pade, perfect system of functions, determinant representation

Full text: PDF file (331 kB)
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UDC: 517.538.52+517.538.53
Received: 02.11.2010

Citation: A. P. Starovoitov, N. V. Rjabchenko, “Determinant representation of Pade joint approximations”, PFMT, 2010, no. 4(5), 46–49

Citation in format AMSBIB
\Bibitem{StaRja10}
\by A.~P.~Starovoitov, N.~V.~Rjabchenko
\paper Determinant representation of Pade joint approximations
\jour PFMT
\yr 2010
\issue 4(5)
\pages 46--49
\mathnet{http://mi.mathnet.ru/pfmt198}


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