id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3687	Aydin Akgun, Fatma; Rhoades, Billy E.	E-J Summability of Orthogonal Series	2020	13	.pdf	application/pdf	3694	208	88	From (3) amn = K ∫ 1 0 µm+α(1− µ)n−m ( n− 1 + α m− 1 + α ) dµ = K ( n− 1 + α m− 1 + α )∫ 1 0 µm+α(1− µ)n−mdµ = K ( n− 1 + α m− 1 + α ) Γ(m+ α+ 1)Γ(n−m+ 1) Γ(n+ α+ 2) = K Γ(n+ α) Γ(m+ α)Γ(n−m+ 1) Γ(m+ α+ 1)Γ(n−m+ 1) Γ(n+ α+ 2) = K (m+ α) (n+ α+ 1)(n+ α) . − h (α) n−1,k (2) = [ ∫ 1 0 µk+α(1− µ)n−k ( n+ α k + α ) dχ(µ)− ∫ 1 0 µk+α(1− µ)n−1−k ( n− 1 + α k + α ) dχ(µ) ] = ∫ 1 0 µk+α(1− µ)n−k [(n+ α k + α ) − ( n− 1 + α k + α ) 1 1− µ ] dχ(µ), where 0 ≤ k ≤ n. Since ( n+ α k + α )	cache/ejpam-3687.pdf	txt/ejpam-3687.txt