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$w_{\\lambda}(t) := (1-t^2)^{\\lambda-1/2}$, where $\\lambda > -\\frac{1}{2}$, be the Gegenbauer weight function, let $\\|\\cdot\\|_{w_{\\lambda}}$ be the associated $L_2$-norm, $$\n  \\|f\\|_{w_{\\lambda}} = \\left\\{\\int_{-1}^1 |f(x)|^2 w_{\\lambda}(x)\\,dx\\right\\}^{1/2}\\,, $$ and denote by $\\mathcal{P}_n$ the space of algebraic polynomials of degree $\\le n$.\n  We study the best constant $c_n(\\lambda)$ in the Markov inequality in this norm $$\n  \\|p_n'\\|_{w_{\\lambda}} \\le c_n(\\lambda) \\|p_n\\|_{w_{\\lambda}}\\,,\\qquad p_n \\in \\mathcal{P}_n\\,, $$ namely the constant $$ c_n(\\lambda) := \\sup_{p_n \\in \\mathcal{","authors_text":"Alexei Shadrin, Geno Nikolov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-01-26T13:15:18Z","title":"On the Markov inequality in the $L_2$-norm with the Gegenbauer 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