Generating functions on extended Jacobi polynomials from Lie group view point.

Mukherjee, Manik Chandra. "Generating functions on extended Jacobi polynomials from Lie group view point.." Publicacions Matemàtiques 40.1 (1996): 3-13. <http://eudml.org/doc/41257>.

@article{Mukherjee1996,
abstract = {Generating functions play a large role in the study of special functions. The present paper deals with the derivation of some novel generating functions of extended Jacobi polynomials by the application of [the] group-theoretic method introduced by Louis Weisner. In fact, by suitably interpreting the index (n) and the parameter (β) of the polynomial under consideration we define four linear partial differential operators and on showing that they generate a Lie-algebra, we obtain a new generating relation (3.3) as the main result of our investigation. Furthermore, some generating functions of Laguerre, Hermite, Bessel and Jacobi polynomials are obtained as the special cases of our main result. Some applications of our results are also pointed out.},
author = {Mukherjee, Manik Chandra},
journal = {Publicacions Matemàtiques},
keywords = {Funciones especiales; Función generatriz; Polinomios de Jacobi; Polinomios de Hermite; Polinomios de Laguerre; generating functions; Jacobi polynomials; Hermite polynomials; Laguerre polynomials; Bessel polynomials},
language = {eng},
number = {1},
pages = {3-13},
title = {Generating functions on extended Jacobi polynomials from Lie group view point.},
url = {http://eudml.org/doc/41257},
volume = {40},
year = {1996},
}

TY - JOUR
AU - Mukherjee, Manik Chandra
TI - Generating functions on extended Jacobi polynomials from Lie group view point.
JO - Publicacions Matemàtiques
PY - 1996
VL - 40
IS - 1
SP - 3
EP - 13
AB - Generating functions play a large role in the study of special functions. The present paper deals with the derivation of some novel generating functions of extended Jacobi polynomials by the application of [the] group-theoretic method introduced by Louis Weisner. In fact, by suitably interpreting the index (n) and the parameter (β) of the polynomial under consideration we define four linear partial differential operators and on showing that they generate a Lie-algebra, we obtain a new generating relation (3.3) as the main result of our investigation. Furthermore, some generating functions of Laguerre, Hermite, Bessel and Jacobi polynomials are obtained as the special cases of our main result. Some applications of our results are also pointed out.
LA - eng
KW - Funciones especiales; Función generatriz; Polinomios de Jacobi; Polinomios de Hermite; Polinomios de Laguerre; generating functions; Jacobi polynomials; Hermite polynomials; Laguerre polynomials; Bessel polynomials
UR - http://eudml.org/doc/41257
ER -