1. CJM 2011 (vol 64 pp. 961)
 Borwein, Jonathan M.; Straub, Armin; Wan, James; Zudilin, Wadim

Densities of Short Uniform Random Walks
We study the densities of uniform random walks in the plane. A special focus
is on the case of short walks with three or four steps and less completely
those with five steps. As one of the main results, we obtain a hypergeometric
representation of the density for four steps, which complements the classical
elliptic representation in the case of three steps. It appears unrealistic
to expect similar results for more than five steps. New results are also
presented concerning the moments of uniform random walks and, in particular,
their derivatives. Relations with Mahler measures are discussed.
Keywords:random walks, hypergeometric functions, Mahler measure Categories:60G50, 33C20, 34M25, 44A10 

2. CJM 2010 (vol 62 pp. 261)
3. CJM 2006 (vol 58 pp. 726)
 Chiang, YikMan; Ismail, Mourad E. H.

On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials
We show that the value distribution (complex oscillation) of
solutions of certain periodic second order ordinary differential
equations studied by Bank, Laine and Langley is closely
related to confluent hypergeometric functions, Bessel functions
and Bessel polynomials. As a result, we give a complete
characterization of the zerodistribution in the sense of
Nevanlinna theory of the solutions for two classes of the ODEs.
Our approach uses special functions and their asymptotics. New
results concerning finiteness of the number of zeros
(finitezeros) problem of Bessel and Coulomb wave functions with
respect to the parameters are also obtained as a consequence. We
demonstrate that the problem for the remaining class of ODEs not
covered by the above ``special function approach" can be
described by a classical Heine problem for differential
equations that admit polynomial solutions.
Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine Proble Categories:34M10, 33C15, 33C47 
