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Unveiling new perspectives of hypergeometric functions using umbral techniques
Giuseppe Dattoli, Mehnaz Haneef, Subuhi Khan +1
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the aut…
Hermite, Higher order Hermite, Laguerre type polynomials and Burgers like equations
Giuseppe Dattoli, Roberto Garra, Silvia Licciardi
The multivariable version of ordinary and generalized Hermite polynomials are the natural solutions of the classical heat equation and of its higher order versions. We derive the a…
Monomiality and a New Family of Hermite Polynomials
Giuseppe Dattoli, Silvia Licciardi
In this article we go deeply into the formulation and meaning of the monomiality principle and employ it to study the properties of a set of polynomials, which, asymptotically, red…
Umbral-Algebraic Methods and Asymptotic Properties of Special Polynomials
G. Dattoli, S. Licciardi, R. M. Pidatella +1
A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, al…
Generating Functions for Lacunary Legendre and Legendre-like Polynomials
S. Licciardi, G. Dattoli, R. M. Pidatell
The use of operational methods of different nature is shown to be a fairly powerful tool to study different problems regarding the theory of Legendre and Legendre-like polynomials.…
Operational vs. Umbral Methods and Borel Transform
Giuseppe Dattoli, Silvia Licciardi
Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special func…