Sheffer and Non-Sheffer Polynomial Families

By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials

Repeated derivatives of hyperbolic trigonometric functions and associated polynomials

Elementary problems as the evaluation of repeated derivatives of ordinary transcendent functionscan usefully be treated with the use of special polynomials and of a formalism borrowed from combinatorial analysis. Motivated by previous researches in this field, we review the results obtained by other authors and develop a complementary point of view for the repeated derivatives of sec(.), tan(.) and for their hyperbolic counterparts

Sheffer and Non-Sheffer Polynomial Families

By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials

A novel theory of Legendre polynomials

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