3 papers
math.CA2026
Connection Formulae for a Generalised Ramanujan Entire Function
Joshua Holroyd
The Ramanujan-Airy connection formula relates the convergent series at the origin to the behaviour at infinity of the Ramanujan entire function. We extend this connection to…
math.CA2025
Elliptic asymptotic behaviour of -Painlevé transcendents
Joshua Holroyd
The discrete Painlevé equations have mathematical properties closely related to those of the differential Painlevé equations. We investigate the appearance of elliptic functions as…
math-ph2022
On the Perturbed Second Painlevé Equation
Joshua Holroyd, Nalini Joshi
We consider a perturbed version of the second Painlevé equation (), which arises in applications, and show that it possesses solutions analogous to the ce…