A characterization of the Rogers -Hermite polynomials.
Al-Salam, Waleed A. (1995)
International Journal of Mathematics and Mathematical Sciences
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Al-Salam, Waleed A. (1995)
International Journal of Mathematics and Mathematical Sciences
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M. Filaseta, T.-Y. Lam (2002)
Acta Arithmetica
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Milovanović, Gradimir V. (1993)
Publications de l'Institut Mathématique. Nouvelle Série
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Wojciech Młotkowski (2006)
Banach Center Publications
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We provide explicit formulas for linearizing coefficients for some class of orthogonal polynomials.
Roberto Dvornicich, Shih Ping Tung, Umberto Zannier (2003)
Acta Arithmetica
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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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Ruedemann, Richard W. (1994)
International Journal of Mathematics and Mathematical Sciences
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A. Pain (1971)
Matematički Vesnik
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Claude Brezinski (1992)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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S. K. Chatterjea (1964)
Rendiconti del Seminario Matematico della Università di Padova
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Milovanović, Gradimir V. (1998)
Publications de l'Institut Mathématique. Nouvelle Série
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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.