On an system of “classical” polynomials of simultaneous orthogonality
Copyright policy )On an system of “classical” polynomials of simultaneous orthogonality
Let \(Q_{\overline n}(x)\), \(\overline n=(n_1,n_2)\), be the system of polynomials of simultaneous orthogonality [see \textit{E. M. Nikishin} and \textit{V. N. Sorokin}: ``Rational approximations and orthogonality'' (Russian orig. 1988; Zbl 0718.41002; Engl. transl. 1991; Zbl 0733.41001)] with \(\Delta_1=[a;0]\), \(\Delta_2=[0;1] (-1\leq a-1)\). The differential equation of third-order, the limit periodic behaviour of recurrence coefficients, and the ratio asymptotics for those polynomials are obtained.
- Gembloux Agro-Bio Tech Belgium
- Université de Namur Belgium
- University of Liège Belgium
- Institute of Applied Mathematics Russian Federation
- Russian Academy of Sciences Russian Federation
Computational Mathematics, Applied Mathematics, Hermite-Padé polynomials, Padé approximations, Simultaneous orthogonality, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Padé approximation, orthogonal polynomials, Differential equations of third order, Difference equations of third order
Computational Mathematics, Applied Mathematics, Hermite-Padé polynomials, Padé approximations, Simultaneous orthogonality, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Padé approximation, orthogonal polynomials, Differential equations of third order, Difference equations of third order
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