**Orthogonality of the big -1 Jacobi polynomials for non-standard parameters**

**Date: **
2023..03..01

**Event: **AMS Spring eastern sectional meeting

**Venue: **
Online, Pacific Time

## Abstract

A study is carried out about the big \(-1\) orthogonal Jacobi polynomials, in particular for non-standard parameters case.

The aim of this work is to obtain the orthogonality property of this family for non-standard parameters. Since these polynomials are orthogonal then they fulfill the recurrence relation

\[ x p_n(x)=\alpha_n p_{n+1}(x)+\beta_n p_n(x)+\gamma_n p_{n-1}(x), \] with initial conditions \(p_0(x)=1\) and \(p_{-1}(x)=0\).We are interested in those cases for which some integer value \(n\) can be found for which the coefficient \(\gamma_n=0\), and therefore Favardâ€™s theorem cannot be directly applied. Is for such a case for which a new proper of orthogonality related to an orthogonality of type \(\Delta\)-Sobolev will be provided.

## Download

Link | Size | Description |
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T30_AMSSPEA.pdf | 252 KB | Slides (PDF, 15 slides) |