3 papers
math.NT2020
Continued fractions for strong Engel series and Lüroth series with signs
Andrew N. W. Hone, Juan Luis Varona
An Engel series is a sum of reciprocals of a non-decreasing sequence of positive integers with the property that divides for all $n\geq…
math.CA2017
Hirota bilinear equations for Painlevé transcendents
A. N. W. Hone, F. Zullo
We present some observations on the tau-function for the fourth Painlevé equation. By considering a Hirota bilinear equation of order four for this tau-function, we describe the ge…
math.CA2012
Properties of the series solution for Painleve I
A. N. W. Hone, O. Ragnisco, F. Zullo
We present some observations on the asymptotic behaviour of the coefficients in the Laurent series expansion of solutions of the first Painleve equation. For the general solution,…