On the $$L^2$$-norm of Gegenbauer polynomials
نویسندگان
چکیده
منابع مشابه
On the Markov inequality in the L2-norm with the Gegenbauer weight
Let wλ(t) := (1− t2)λ−1/2, where λ > − 12 , be the Gegenbauer weight function, let ‖ · ‖wλ be the associated L2-norm, ‖f‖wλ = {∫ 1 −1 |f(x)|wλ(x) dx }1/2 , and denote by Pn the space of algebraic polynomials of degree≤ n. We study the best constant cn(λ) in the Markov inequality in this norm ‖pn‖wλ ≤ cn(λ)‖pn‖wλ , pn ∈ Pn , namely the constant cn(λ) := sup pn∈Pn ‖pn‖wλ ‖pn‖wλ . We derive explic...
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ژورنال
عنوان ژورنال: Mathematical Sciences
سال: 2021
ISSN: 2008-1359,2251-7456
DOI: 10.1007/s40096-021-00398-1