Open AccessFrom special operators (1-Dx )n+α to Laguerre Polynomials
Publication year - 2021
Publication title -
advances in theoretical and computational physics
Language(s) - English
Resource type - Journals
ISSN - 2639-0108
DOI - 10.33140/atcp.04.03.05
Subject(s) - laguerre polynomials , mathematics , special functions , operator (biology) , classical orthogonal polynomials , orthogonal polynomials , algebra over a field , monomial , orthogonality , pure mathematics , discrete mathematics , chemistry , biochemistry , repressor , transcription factor , gene , geometry
Laguerre polynomials Ln α (x) are shown to be the transforms of monomials by the special operators (1-Dx )n+α . From this their current properties such as Rodrigues formula, Lucas symbolic formula, orthogonality, generating functions, etc… are systematically obtained. This success opens the way for the study of special functions from special operators by the powerful operator calculus.