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On expansions of functions of two variables in mixed Fourier–Jacobi series and their application for estimation of errors of cubature formulas

V. A. Abilov^a, G. A. Djalaeva^a, M. K. Kerimov<sup>b

a</sup> Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia
^b Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, GSP-1, Moscow, 119991, Russia

Abstract: Some problems of expansion of functions of two variables in mixed Fourier–Jacobi series are discussed. In particular, estimates of the convergence rate of these series on classes of functions of two variables characterized by generalized moduli of continuity are given. Applications of these results and estimation of residues of some Chebyshev-type mixed cubature formulas are discussed.

Key words: mixed Fourier–Jacobi series, convergence problems, estimates of residual terms, diameters, absolute convergence conditions.

UDC: 517.518.475+519.644.7

Received: 16.03.2007

 English version: Computational Mathematics and Mathematical Physics, 2007, 47:8, 1243–1252

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