Ryu Sasaki, Kouchi Takemura, “Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity”, SIGMA, 2012, Volume 8,085, 18 pp.

This article is cited in 10 papers

Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity

Ryu Sasaki^a, Kouchi Takemura^b

^a Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
^b Department of Mathematics, Faculty of Science and Technology, Chuo University, 1-13-27 Kasuga, Bunkyo-ku Tokyo 112-8551, Japan

Abstract: Infinitely many explicit solutions of certain second-order differential equations with an apparent singularity of characteristic exponent $-2$ are constructed by adjusting the parameter of the multi-indexed Laguerre polynomials.

Keywords: multi-indexed orthogonal polynomials; solvable systems; Fuchsian differential equations; Heun's equation; apparent singularities; high characteristic exponents.

MSC: 33C45; 33C47

Received: July 24, 2012; in final form November 7, 2012; Published online November 15, 2012

Language: English

DOI: 10.3842/SIGMA.2012.085