AIMSVSW 2018: Orthogonal Polynomials pp 25-43

# Classical Continuous Orthogonal Polynomials

• Salifou Mboutngam
Conference paper
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)

## Abstract

Classical orthogonal polynomials (Hermite, Laguerre, Jacobi and Bessel) constitute the most important families of orthogonal polynomials. They appear in mathematical physics when Sturn-Liouville problems for hypergeometric differential equation are studied. These families of orthogonal polynomials have specific properties. Our main aim is to:
1. 1.

recall the definition of classical continuous orthogonal polynomials;

2. 2.

prove the orthogonality of the sequence of the derivatives;

3. 3.

prove that each element of the classical orthogonal polynomial sequence satisfies a second-order linear homogeneous differential equation;

4. 4.

give the Rodrigues formula.

## Keywords

Classical orthogonal polynomials Rodrigues formula Differential equation Pearson type equation

33C45 33D45

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