Polinomios ultraesféricos

Abstract

In the present document are studied ultraspherical polynomials as a particular case of Jacobi Polynomials. First of all general theory of orthogonal polynomial systems is studied respect to a moment functional, so that is seen the di erent properties and characteristics of an orthogonal polynomial system and its recurrence formula for three terms. In the next part is introduced some special functions as Gamma function, Beta function, hypergeometric function and Pochhammer factorial to de ne Jacobi Polynomials, below is shown which is the moment functional that turns Jacobi polynomials into an orthogonal polynomial system, then is studied some di erential properties and is characterized its recurrence formula. Finally is de ned the ultraspherical polynomials based on Jacobi polynomials, is displayed the moment functional that turns ultraspherical polynomial into orthogonal system, its recurrence formula and classic examples as Legendre polynomials, Chebyshev polynomials of rst and second order.