Theory of Orthogonal Polynomials and Construction of Differential Operators with Orthogonal Polynomials as Eigenfunction

Abstract

The subject of orthogonal polynomials is a classical one whose origins can be traced to Legendre’s work on planetary motion. With important applications to physics and to probability and statistics and other branches of mathemat- ics, the subject flourished through the first half of this century. Orthogonal Polynomials are special class of polynomials which are useful in studying var- ious physical and mathematical problems. They occur naturally as solution to many important differential equations arising from physical phenomenon and thus making them an interesting topic. In this thesis I shall aim to cover basics of Orthogonal Polynomials in general and discuss the recent technique to construct differential operator corresponding to a specific class of orthog- onal polynomials which have these as eigen functions. Further an example has been illustrated using the theory discussed.