Sesión Geometría Algebraica y Teoría de Números

Diciembre 15, 16:10 ~ 16:30

Appell polynomials as values of special functions

Varona, Juan L.

We show that there is a large class of Appell sequences $\{P_{n}(x)\}_{n=0}^{\infty}$ for which there is a function $F(s,x)$, entire in $s$ for fixed $x$ with $\operatorname{Re} x > 0$ and satisfying $F(-n,x) = P_{n}(x)$ for $n=0,1,2,\dots$. For example, in the case of Bernoulli and Apostol-Bernoulli polynomials, $F$ is essentially the Hurwitz zeta function and the Lerch transcendent, respectively. We study a subclass of these Appell sequences for which the corresponding special function has a form more closely related to the classical zeta functions, and give some interesting examples of these general constructions.

Autores: Navas, Luis M. / Ruiz, Francisco J. / Varona, Juan L. .