17 citations · 48 across the 21 of their papers we have counts for
9 papers · 1 filter
Holonomic Bessel modules and generating functions
Yik Man Chiang, Avery Ching, Xiaoli Lin
We have solved a number of holonomic PDEs derived from the Bessel modules which are related to the generating functions of classical Bessel functions and the difference Bessel func…
Series solutions of linear ODEs by Newton-Raphson method on quotient -modules
Yik Man Chiang, Avery Ching, Chiu Yin Tsang
We develop a module approach to various kinds of solutions to several classes of important differential equations by long divisions of different differential operators. The zer…
Resolving singularities and monodromy reduction of Fuchsian connections
Yik-Man Chiang, Avery Ching, Chiu-Yin Tsang
We study monodromy reduction of Fuchsian connections from a sheave theoretic viewpoint, focusing on the case when a singularity of a special connection with four singularities has…
Invariant subspaces of biconfluent Heun operators and special solutions of Painlevé IV
Yik-Man Chiang, Chun-Kong Law, Guo-Fu Yu
We show that there is a full correspondence between the parameters space of the degenerate biconfluent Heun connection (BHC) and that of Painlevé IV that admits special solutions.…
Solutions of Darboux Equations, its Degeneration and Painlevé VI Equations
Yik-Man Chiang, Avery Ching, Chiu-Yin Tsang
In this paper, we study the Darboux equations in both classical and system form, which give the elliptic Painlevé VI equations by the isomonodromy deformation method. Then we estab…
Galoisian approach to complex oscillation theory of some Hill equations
Yik-Man Chiang, Guo-Fu Yu
We apply Kovacic's algorithm from differential Galois theory to show that all complex non-oscillatory solutions (finite exponential of convergence of zeros) of certain Hill equatio…