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An inequality for Tchebycheff polynomials and extensions. (English) Zbl 0297.33018

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
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[1] Askey, R.; Gasper, G., Jacobi polynomial expansions of Jacobi polynomials with non-negative coefficients, (Proc. Cambridge Philos. Soc., 70 (1971)), 243-255 · Zbl 0217.11402
[2] Erdélyi, A., (Higher Transcendental Functions, vol. 1 (1953), McGraw-Hill: McGraw-Hill New York)
[3] Erdélyi, A., (Higher Transcendental Functions, vol. 2 (1953), McGraw-Hill: McGraw-Hill New York)
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[5] Gasper, G., On two conjectures of Askey concerning normalized Hankel determinants for the classical polynomials, SIAM J. Math. Anal., 4, 508-513 (1973) · Zbl 0256.33016
[6] Gegenbauer, L., Zur Theorie der Funktionen \(C_n^{ pv }(x)\), Denksch. Akad. Wiss. Wien, Math. Natur. Klasse, 48, 293-316 (1884) · JFM 16.0452.02
[7] Koornwinder, T. H., The addition formula for Jacobi polynomials, I, Summary of results, Indag. Math., 34, 188-191 (1972) · Zbl 0247.33017
[8] Malkov, E. I., Yad. Fiz., 10, 849-855 (1969)
[9] Rogosinski, W. W., Some elementary inequalities for polynomials, Math. Gaz., 39, 7-12 (1955) · Zbl 0064.01802
[10] Schur, I., Über das Maximum des absoluten Betrages eines Polynoms in einem gegebenen Intervall, Math. Z., 4, 271-287 (1919) · JFM 47.0249.02
[11] Szegö, G., Orthogonal Polynomials, (Amer. Math. Soc. Colloq. Pub., vol. 23 (1967), American Mathematical Society: American Mathematical Society Providence, RI) · JFM 65.0278.03
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