Geodesic
Finite Limit Series on Chebyshev Polynomials, Orthogonal on Uniform Nets
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 104-108 
T. I. Sharapudinov. Finite Limit Series on Chebyshev Polynomials, Orthogonal on Uniform Nets. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 1, pp. 104-108. http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a25/
@article{ISU_2013_13_1_a25,
     author = {T. I. Sharapudinov},
     title = {Finite {Limit} {Series} on {Chebyshev} {Polynomials,} {Orthogonal} on {Uniform} {Nets}},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {104--108},
     year = {2013},
     volume = {13},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a25/}
}
TY  - JOUR
AU  - T. I. Sharapudinov
TI  - Finite Limit Series on Chebyshev Polynomials, Orthogonal on Uniform Nets
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2013
SP  - 104
EP  - 108
VL  - 13
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a25/
LA  - ru
ID  - ISU_2013_13_1_a25
ER  - 
%0 Journal Article
%A T. I. Sharapudinov
%T Finite Limit Series on Chebyshev Polynomials, Orthogonal on Uniform Nets
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2013
%P 104-108
%V 13
%N 1
%U http://geodesic.mathdoc.fr/item/ISU_2013_13_1_a25/
%G ru
%F ISU_2013_13_1_a25

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper we construct new series, called finite limit series on Chebyshev (Hahn) polynomials $\tau^{\alpha,\beta}_n(x)=\tau^{\alpha,\beta}_n(x,N)$, orthogonal on uniform net $\{0,1,\ldots,N-1\}$. Their partial sums $S_n(f;x)$ equal in boundary points $x=0$ и $x=N-1$ with approximated function $f(x)$. Construction of finite limit series based on the passage to the limit with $\alpha\to-1$ of Fourier series $\sum\limits_{k=0}^{N-1}f_k^\alpha \tau_k^{\alpha,\alpha}(x,N)$ on Chebyshev (Hahn) polynomials $\tau_n^{\alpha,\alpha}(x,N)$, orthonormal on uniform net $\{0,1,\ldots,N-1\}$.

[1] Sharapudinov I. I., Mixed series of orthogonal polynomials. Theory and applications, Dagestan. nauch. center RAN, Makhachkala, 2004, 276 pp.