Abstract
Let ‖·‖ be the weightedL 2-norm with weightw(t). LetP n be the set of all complex polynomials whose degree does not exceedn and let\(\gamma _n^{(r)} : = \sup _{f \in P_n } \) (‖f (r)‖/‖f‖). In this paper we given upper and lower bound for γ (r)n in the case of the Laguerre weight functionw(t)=exp (−t) and investigate its behaviour asn→∞. Moreover, we derive some identities concerningorthogonal polynomials.
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Dörfler, P. A markov type inequality for higher derivatives of polynomials. Monatshefte für Mathematik 109, 113–122 (1990). https://doi.org/10.1007/BF01302931
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DOI: https://doi.org/10.1007/BF01302931