Characterization of generalized Bessel polynomials in terms of polynomial inequalities. (English) Zbl 0911.33004
The authors prove two theorems, each of which characterizes the generalized Bessel polynomials \(y_n(x;\alpha,\beta)\) as the extremal polynomials in certain interesting inequalities of Markov type in an \(L^2\) norm. Their results are based upon an orthogonality property of the generalized Bessel polynomials, which was considered earlier by the reviewer [Appl. Math. Comput. 61, No. 2-3, 99–134 (1994; Zbl 0791.33006)].
Reviewer: Hari M. Srivastava (Victoria)
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
Bessel polynomialsCitations:
Zbl 0791.33006References:
| [1] | Dimitrov, D. K., Bernstein inequality in \(L_2\), Math. Balkanica (N.S.), 7, 131-136 (1993) · Zbl 0830.41011 |
| [2] | Guessab, A.; Milovanović, G. V., Weighted \(L^2\), J. Math. Anal. Appl., 182, 244-249 (1994) · Zbl 0799.41017 |
| [3] | Milovanović, G. V.; Mitrinović, D. S.; Rassias, Th. M., Topics in Polynomials: Extremal Problems, Inequalities, Zeros (1994), World Scientific: World Scientific Singapore · Zbl 0848.26001 |
| [4] | Min, G. H., Bernstein-Markov inequalities in \(L^2\), J. Math. Res. Exposition, 14, 135-138 (1994) · Zbl 0830.41012 |
| [5] | Srivastava, H. M., Orthogonality relations and generating functions for the generalized Bessel polynomials, Appl. Math. Comput., 61, 99-134 (1994) · Zbl 0791.33006 |
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