We reformulate the theory of Legendre polynomials using the method of integral transforms, which allow us to express them in terms of Hermite polynomials. We show that this allows a self consistent point of view to their relevant properties and the possibility of framing generalized forms like the Humbert polynomials within the same framework. The multi-index multi-variable case is touched on. (C) 2011 Elsevier Ltd. All rights reserved.
A novel theory of Legendre polynomials / Martinelli, Maria Renata; G., Dattoli; Germano, Bruna; Ricci, Paolo Emilio. - In: MATHEMATICAL AND COMPUTER MODELLING. - ISSN 0895-7177. - 54:1-2(2011), pp. 80-87. [10.1016/j.mcm.2011.01.037]
A novel theory of Legendre polynomials
MARTINELLI, Maria Renata;GERMANO, Bruna;RICCI, Paolo Emilio
2011
Abstract
We reformulate the theory of Legendre polynomials using the method of integral transforms, which allow us to express them in terms of Hermite polynomials. We show that this allows a self consistent point of view to their relevant properties and the possibility of framing generalized forms like the Humbert polynomials within the same framework. The multi-index multi-variable case is touched on. (C) 2011 Elsevier Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
