### An estimate for coefficients of polynomials in ${L}^{2}$ norm. II.

Milovanović, G.V., Rančić, L.Z. (1995)

Publications de l'Institut Mathématique. Nouvelle Série

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Milovanović, G.V., Rančić, L.Z. (1995)

Publications de l'Institut Mathématique. Nouvelle Série

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Roberto Dvornicich, Shih Ping Tung, Umberto Zannier (2003)

Acta Arithmetica

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Milovanović, Gradimir V. (1998)

Publications de l'Institut Mathématique. Nouvelle Série

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Al-Salam, Waleed A. (1995)

International Journal of Mathematics and Mathematical Sciences

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Norris Sookoo (2000)

Archivum Mathematicum

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Orthogonality conditions and recurrence relations are presented for generalized Krawtchouk polynomials. Coefficients are evaluated for the expansion of an arbitrary polynomial in terms of these polynomials and certain special values for generalized Krawtchouk polynomials are obtained. Summations of some of these polynomials and of certain products are also considered.

D. P. Shukla (1979)

Matematički Vesnik

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Shukla, D.P. (1981)

Publications de l'Institut Mathématique. Nouvelle Série

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Agrawal, Hukum Chand (1983)

Publications de l'Institut Mathématique. Nouvelle Série

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David Dickinson (1958)

Bollettino dell'Unione Matematica Italiana

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James McKee, Chris Smyth (2013)

Open Mathematics

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We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class,...

Rhin, G., Sac-Épée, J.-M. (2003)

Experimental Mathematics

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Hans Weber (2007)

Open Mathematics

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A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.