Nonlinear Integral-Equation Formulation of Orthogonal Polynomials
| dc.creator | Bender, Carl M. | |
| dc.creator | Ben-Naim, E. | |
| dc.date | 2006-10-26 | |
| dc.date | 2006-11-15 | |
| dc.date.accessioned | 2026-07-07T07:28:29Z | |
| dc.date.available | 2026-07-07T07:28:29Z | |
| dc.description | The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial solutions is orthogonal with respect to the measure x w(x). The nonlinear integral equation can be used to specify all orthogonal polynomials in a simple and compact way. This integral equation provides a natural vehicle for extending the theory of orthogonal polynomials into the complex domain. Generalizations of the integral equation are discussed. | |
| dc.description | 7 pages, result generalized to include integration in the complex domain | |
| dc.identifier | https://arxiv.org/abs/math-ph/0610071 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0610071 | |
| dc.identifier | J. Phys. A 40, F9 (2007) | |
| dc.identifier | doi:10.1088/1751-8113/40/1/F02 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117751 | |
| dc.subject | Mathematical Physics | |
| dc.subject | General Mathematics | |
| dc.title | Nonlinear Integral-Equation Formulation of Orthogonal Polynomials | |
| dc.type | text |