Abstract
We study the problem to determine the degree of approximation of \(f\in L[0, \infty )\) by Cesàro means of order \(\lambda \ge 1\) of the Fourier–Laguerre series of f for any \(x >0.\) We prove the result for \(x=0\) separately.
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References
Mäkilä PM (1990) Laguerre series approximation of infinite dimensional systems. Automatica 26(6):985–995
Szegö G (1939) Orthogonal polynomials. American Mathematical Society, New York
Gupta DP (1971) Degree of approximation by Cesàro means of Fourier–Laguerre expansions. Acta Sci Math 32:255–259
Khatri K, Mishra VN (2016) Approximation of functions belonging to \(L[0,\infty )\) by product summability means of its Fourier–Laguerre series. Cogent Math Stat 3(1):1250854
Krasniqi XZ (2013) On the degree of approximation of a function by \((C, 1)(E, q)\) means of its Fourier–Laguerre series means. Int J Anal Appl 1(1):33–39
Łenski W, Szal B (2018) Pointwise convergence of Fourier-Laguerre series of integrable functions. Fasciculi Mathematici 60:93–101
Nigam HK, Sharma A (2010) A study on degree of approximation by \((E,1)\) summability means of the Fourier–Laguerre expansion. Int J Math Math Sci. https://doi.org/10.1155/2010/351016
Saini S, Singh U (2015) Degree of approximation of \(f\in L[0,\infty )\) by means of Fourier–Laguerre series. Mathematical Analysis and Its Applications, vol 143. Springer, New Delhi, pp 207–217
Singh T (1978) Degree of approximation by Cesàro means of Fourier–Laguerre series. Indian J Pure Appl Math 9(4):394–399
Tiwari SK, Kachhara DK (2010) Degree of approximation by Nörlund summability means of Laguerre series. J Indian Math Soc 77(1–4):207–213
Singh T (1976) On the absolute summability factors of Fourier–Laguerre expansion. Indian J Pure Appl Math 7(9):961–968
Acknowledgements
This research was supported by Science & Engineering Research Board, Government of India vide Grant No. SB/EMEQ-454/2014.
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Singh, U., Saini, S. Uniform Approximation in \(L[0,\infty )\)-Space by Cesàro Means of Fourier–Laguerre Series. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 92, 179–185 (2022). https://doi.org/10.1007/s40010-021-00747-8
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DOI: https://doi.org/10.1007/s40010-021-00747-8