Ortogonale Polynomier og Rodriguesformlen

Studenteropgave: Speciale (inkl. HD afgangsprojekt)

  • Kristian Nørgaard Jakobsen
4. semester, Matematik, Kandidat (Kandidatuddannelse)
This masters thesis in mathematics is about orthogonal polynomials and their Rodrigues formulas. Some elementary theory on orthogonal polynomial sequences are presented for instance results regarding the recurrence formula which is a formula for deriving orthogonal polynomials recursively. There exist different kinds of orthogonal polynomials with their own interval and weight function for which the polynomials are orthogonal. Three of these families of orthogonal polynomials are also presented in this paper. For these polynomials it is shown that they along with their respecive Rodriguesformula are solutions to the associated second order differential equation. Because of this fact theorems on solutions for these differential equations are addressed on the basis of the generalized Rodrigues formula.
Udgivelsesdato8 jun. 2017
Antal sider39
ID: 259419074