On Zeros Of Laguerre Polynomials

Scientific Essay from the year 2011 in the subject Mathematics - Algebra, language: English, abstract: In this work, we make an attempt to gather different results by many mathematicians who have made landmark achievements in studies on zeros of Laguerre polynomials. We discuss bounds for extreme zeros of some classical orthogonal polynomials, bounds for zeros of the Laguerre polynomials where we quote the works of Ilia Krasikov, among others. The quoted works are: "Limit relation for the complex zeros of Laguerre polynomials", "On the Asymptotic Distribution of the Zeros of Laguerre Polynomials", "Monotonicity of zeros of Laguerre polynomials", "Zeros of linear combinations of Laguerre polynomials from different sequences", "Linear combinations of Laguerre polynomials of the same degree", "Linear combinations of Laguerre polynomials of different degree" and "Convexity of the extreme zeros of Laguerre polynomials".