Geodesic
Approximative properties of mixed series by Lagerre's polynomials onclasses of smooth functions
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 2, pp. 3-11.

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Approximative properties of mixed series by Lagerre's polynomials on classes of smooth functions that given on axle $[0,\infty)$ are viewed. Inequality that corresponds to Lebesgue inequality for trigonometric Fourier sumswas found for evaluation of deflection of smooth function from it's partial sums of mixed series by Lagerre's polynomials. Evaluations for corresponding Lebesgue function of partial sums of mixed series by Lagerre's polynomials were found. 
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S. Ya. Pirmetova. Approximative properties of mixed series by Lagerre's polynomials onclasses of smooth functions. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 2, pp. 3-11. http://geodesic.mathdoc.fr/item/ISU_2008_8_2_a0/

[1] Sharapudinov I. I., “Smeshannye ryady po ortogonalnym polinomam”, Teoriya i prilozheniya, Makhachkala, 2004

[2] Sharapudinov I. I., “Ispravlennye summy Fure po ortogonalnym polinomam i ikh approksimativnye svoistva”, Sovremennye metody teorii funktsii i smezhnye problemy, Tez. dokl. Voronezh. zimnei mat. shkoly (27 yanvarya – 4 fevralya 2001 g.), Izd-vo Voronezh. gos. un-ta, Voronezh, 1999, 289–290

[3] Sharapudinov I. I., “Smeshannye ryady po ortogonalnym polinomam”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tez. dokl. 10-i Sarat. zimnei shkoly, Izd-vo Sarat. un-ta, Saratov, 2000, 228–229

[4] Sege G., Ortogonalnye mnogochleny, izmatgiz, M., 1962

[5] Askey R., Wainger S., “Mean convergence of expansions in Lagerre and Hermite series”, Amer. J. Mathem., 87 (1965), 695–708 | DOI | MR | Zbl

[6] Muckenhaupt B., “Mean convergence of Hermit and Lagerre series. I”, Trans. Amer. Mathem. Soc., 147 (1970), 419–431 | DOI

[7] Muckenhaupt B., “Mean convergence of Hermit and Lagerre series. II”, Trans. Amer. Mathem. Soc., 147 (1970), 433–460 | DOI | MR