A NOTE ON GEGENBAUER POLYNOMIALS
Abstract
The main objective of this work is to study some properties which satisfy differential properties of the Gegenbauer orthogonal polynomials fP(l)
n (x)g with n 2 N and l > 1 2 real, as the differential equation, Rodrigues formula, norm, derivative of order one. Furthermore, we show some algebraic properties such as explicit expression, principal coefficient, recurrence formula three terms and the Christoffel-Darboux formula.
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Alegríıa, P: Teoría de la medida. (2007).
Buyarov, Martínez-Finkelshtein, A: Information entropy of Gegenbauer polynomials J. Phys. A, Math. Gen (2000).
Chihara, TS: An Introduction to Orthogonal polynomials.Gordon and Breach, Science Publisher Inc., New York, EEUU (1978)
De Vicente, Jl, Sánchez-Ruiz, J: Information entropy of Gegenbauer polynomials of integer parameter. J. Phys. A, Math. Gen (2003).
Erdélyi, A, Magnus, W, Oberhettinger, F, Tricomi, F: Higher Trascendental Functions. Vol 3 (1953).
López , G, Pijeira, H: Polinomios Ortogonales. XIV Escuela Venezolana de Matemáticas, Mérida, Venezuela. (2001).
Marcellán, F., Quintana, Y., Urieles, A.: “On the Pollard decomposition method applied to some Jacobi - Sobolev expansions”, T¨ ubitak, Turkish Journal of Mathematics, 934-948 (2013).
Marcellán, F., Quintana, Y.: Polinomios ortogonales no estándar. Propiedades algebraicas y anal´ıticas. XXII Jornadas Venezolanas de Matemáticas (2009).
Pollard, H: The mean convergence of orthogonal series II. Trans. Amer. Math. soc (1948).
Rainville, ED: Special Functions. Macmillan Company, New York (1960); Reprinted by Chelsea publishing Company, Bronx (1971)
Sánchez-Ruiz, J: Information entropy of Gegenbauer polynomials
and Gaussian quadrature. J. Phys. A, Math. Theor. (2007).
Szego, G: Ortogonal Polynomials. Gabor Szego. vol XXIII (1975).
Wing, GM: The mean convergence of orthogonal series. Amer. J. Math. soc (1950).
