Geodesic
On expansions of functions of two variables in mixed Fourier–Jacobi series and their application for estimation of errors of cubature formulas
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 8, pp. 1298-1307

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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. 
@article{ZVMMF_2007_47_8_a2,
     author = {V. A. Abilov and G. A. Djalaeva and M. K. Kerimov},
     title = {On expansions of functions of two variables in mixed {Fourier{\textendash}Jacobi} series and their application for estimation of errors of cubature formulas},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1298--1307},
     publisher = {mathdoc},
     volume = {47},
     number = {8},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_8_a2/}
}
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V. A. Abilov; G. A. Djalaeva; M. K. Kerimov. On expansions of functions of two variables in mixed Fourier–Jacobi series and their application for estimation of errors of cubature formulas. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 8, pp. 1298-1307. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_8_a2/