Geodesic
Rational approximations of Laurent series
Problemy fiziki, matematiki i tehniki, no. 1 (2024), pp. 68-73

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А new scheme for approximating Laurent series with rational functions is investigated. The concept of a generalized polynomial is introduced, and building upon this, a corresponding Padé problem for the Laurent series is formulated and solved. A constructive solution to this problem enables the determination of rational functions, which are then considered as Padé approximations of the Laurent series. It has been established that in the simplest case, these specific Padé approximations of the Laurent series behave similarly to the classical Padé approximations of power series: they localize the singular points of the function that is the sum of the Laurent series.
Keywords: Padé polynomials, power series, Fabry’s theorem.
Mots-clés : Laurent series, Padé–Laurent problem 
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     author = {A. P. Starovoitov and N. V. Ryabchenko},
     title = {Rational approximations of {Laurent} series},
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A. P. Starovoitov; N. V. Ryabchenko. Rational approximations of Laurent series. Problemy fiziki, matematiki i tehniki, no. 1 (2024), pp. 68-73. http://geodesic.mathdoc.fr/item/PFMT_2024_1_a9/