On Bernstein's inequality for ultraspherical polynomials

Archiv der Mathematik

Volumn 69, Issue 6, 1997, Pages 487-490

  Alzer, Horst ^a  

^a NONE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031283621     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000130050150     Document Type: Article

References (9)

1. G. D. ANDERSON, R. W. BARNARD, K. C. RICHARDS, M. K. VAMANAMURTHY and M. K. VUORINEN, Inequalities for zero-balanced hypergeometric functions. Trans. Amer. Math. Soc. 347, 1713-1723 (1995).
2. S. BERNSTEIN, Sur les polynômes orthogonaux relatifs àun segment fini. J Math. 10, 219-286 (1931).
3. Y. CHOW, L. GATTESCHI and R. WONG, A Bernstein-type inequality for the Jacobi polynomial, Proc. Amer. Math. Soc. 121, 703-709 (1994).
4. G. M. FICHTENHOLZ, Differential- und Integralrechnung, II. Berlin 1979.
5. W. GAUTSCHI, Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38, 77-81 (1959).
6. A. LAFORGIA, A simple proof of the Bernstein inequality for ultraspherical polynomials, Boll. Un. Mat. Ital. 6 A, 257-269 (1992).
7. L. LORCH, Inequalities for ultraspherical polynomials and the gamma function. J. Approx. Theory 40, 115-120 (1984).
8. G. V. MILOVANOVIĆ D. S. MITRINOVIĆ and TH. M. RASSIAS, Topics in Polynomials: Extremal Problems, Inequalities, Zeros. Singapore 1994.
9. G. SZEGÖ, Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publ. 1959.