Confluent functions, Laguerre polynomials and their (generalized) bilinear integrals

Autor:	Dereziński, Jan, Gaß, Christian, Vättö, Joonas Mikael
Rok vydání:	2024
Předmět:	Mathematics - Classical Analysis and ODEs 33C45
Druh dokumentu:	Working Paper
Popis:	We review properties of confluent functions and the closely related Laguerre polynomials, and determine their bilinear integrals. As is well-known, these integrals are convergent only for a limited range of parameters. However, when one uses the generalized integral they can be computed essentially without restricting the parameters. This gives the (generalized) Gram matrix of Laguerre polynomials. If the parameters are not negative integers, then Laguerre polynomials are orthogonal, or at least pseudo-orthogonal in the case of generalized integrals. For negative integer parameters, the orthogonality relations are more complicated. Comment: 21 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.16539 Zobrazit plný text záznamu View this record from Arxiv