{"paper":{"title":"Estimates for the best constant in a Markov $L_2$-inequality with the assistance of computer algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Geno Nikolov, Rumen Uluchev","submitted_at":"2017-11-20T16:41:08Z","abstract_excerpt":"We prove two-sided estimates for the best (i.e., the smallest possible) constant $\\,c_n(\\alpha)\\,$ in the Markov inequality $$\n  \\|p_n'\\|_{w_\\alpha} \\le c_n(\\alpha) \\|p_n\\|_{w_\\alpha}\\,, \\qquad p_n \\in {\\cal P}_n\\,. $$ Here, ${\\cal P}_n$ stands for the set of algebraic polynomials of degree $\\le n$, $\\,w_\\alpha(x) := x^{\\alpha}\\,e^{-x}$, $\\,\\alpha > -1$, is the Laguerre weight function, and $\\|\\cdot\\|_{w_\\alpha}$ is the associated $L_2$-norm, $$\n  \\|f\\|_{w_\\alpha} = \\left(\\int_{0}^{\\infty} |f(x)|^2 w_\\alpha(x)\\,dx\\right)^{1/2}\\,. $$ Our approach is based on the fact that $\\,c_n^{-2}(\\alpha)\\,$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07398","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}