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SIGMA 8 (2012), 085, 18 pages arXiv:1207.5302
https://doi.org/10.3842/SIGMA.2012.085
Contribution to the Special Issue “Superintegrability, Exact Solvability, and Special Functions”
Global Solutions of Certain Second-Order Differential Equations with a High Degree of Apparent Singularity
Ryu Sasaki a and Kouichi 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
Received July 24, 2012, in final form November 07, 2012; Published online November 15, 2012
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.
Key words:
multi-indexed orthogonal polynomials; solvable systems; Fuchsian differential equations; Heun's equation; apparent singularities; high characteristic exponents.
pdf (409 kb)
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