Abstract
A new note on factored infinite series and trigonometric Fourier series
Highlights
Let an be a given infinite series with the partial sums
Many works dealing with the absolute summability factors of infinite series and Fourier series have been done
As in Tn,1, we have that m+1 n=2
Summary
By tnα we denote the nth Cesàro mean of order α, with α > −1, of the sequence (nan), that is (see [21]). Let (pn) be a sequence of positive real numbers such that n. (Xn) is a positive increasing sequence tending to infinity as n → ∞. The series an is said to be summable |N , pn|k , k ≥ 1, if (see [3]). K = 1), |N , pn|k summability is the same as |C , 1|k For any sequence (λn ) we write that ∆2λn = ∆λn − ∆λn+1 and ∆λn = λn − λn+1. The sequence (λn) is said to be of bounded variation, denoted by (λn) ∈ BV , if
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