Degree of Approximation of $$f\in L[0,\infty )$$ by Means of Fourier–Laguerre Series

Abstract

In this paper, we determine the degree of approximation of functions belonging to \( L[0,\infty )\) by the Hausdorff means of its Fourier–Laguerre series at \(x=0.\) Our theorem extends some of the recent results of Nigam and Sharma [A study on degree of approximation by (E, 1) summability means of the Fourier–Laguerre expansion, Int. J. Math. Math. Sci. (2010), Art. ID 351016, 7], Krasniqi [On the degree of approximation of a function by (C, 1)(E, q) means of its Fourier–Laguerre series, International Journal of Analysis and Applications 1 (2013), 33–39] and Sonker [Approximation of Functions by (C, 2)(E, q) means of its Fourier–Laguerre series, Proceeding of ICMS-2014 ISBN 978-93-5107-261-4:125–128.] in the sense that the summability methods used by these authors have been replaced by the Hausdorff matrices.