Speaker
Prof.
Tibor Poganj
(University of Rijeka, Croatia)
Description
The first story concerns the real integral expression for the normalization constant $Z(\lambda, \nu)$ which occurs in the Conway-Maxwell distribution which is a generalization of the Poisson law. It turns out that $Z(\lambda, \nu)$ can be connected to the Le Roy-type hypergeometric function.
The second part of the talk resolves the representation of the Pólya constant in terms of Lauriella generalized hypergeometric function $F_C^{(d)}$ of $d$ variables. The Pólya constant describes the probability $p(d)$ that a simple symmetric random walk on the $d$-dimensional lattice $\mathbb Z^d$ returns to origin, for $d \in \mathbb N$. A famous 103 years old result of Pólya states that $p(1) = p(2) = 1$ but $p(d) < 1$ for $d \geq 3$.
Primary author
Prof.
Tibor Poganj
(University of Rijeka, Croatia)
