313 citations · 679 across the 35 of their papers we have counts for
4 papers · 2 filters
Heun functions versus elliptic functions
Galliano Valent
We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard's generalization of Floquet's theory for…
From asymptotics to spectral measures: determinate versus indeterminate moment problems
Galliano Valent
In the field of orthogonal polynomials theory, the classical Markov theorem shows that for determinate moment problems the spectral measure is under control of the polynomials asym…
Neumann-like integrable models
Galliano Valent, Hamed Ben Yahia
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For we recover Neumann…
Some cubic birth and death processes and their related orthogonal polynomials
Jacek Gilewicz, Elie Leopold, Andreas Ruffing +1
The orthogonal polynomials with recurrence relation \[(\la\_n+μ\_n-z) F\_n(z)=μ\_{n+1} F\_{n+1}(z)+\la\_{n-1} F\_{n-1}(z)\] with two kinds of cubic transition rates $\la\_n$ and $μ…