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math.CA2019★ 2 cited
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.…
math.CA2016★ 3 cited
A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation
Peter A. Clarkson, Chun-Kong Law, Chia-Hua Lin
We are concerned with the Umemura polynomials associated with rational solutions of the third Painlevé equation. We extend Taneda's method, which was developed for the Yablonskii-V…