TY - JOUR

T1 - On the Umemura polynomials for the Painlevé III equation

AU - Kajiwara, Kenji

AU - Masuda, Tetsu

N1 - Funding Information:
The authors would like to thank Prof. M. Noumi and Prof. Y. Yamada for discussions. They also thank Prof. H. Umemura for encouragement. One of the authors (K.K.) is supported by the Grant-in-aid for Encouragement of Young Scientists, The Ministry of Education, Science and Culture of Japan, No. 09740164.

PY - 1999/9/27

Y1 - 1999/9/27

N2 - A determinant expression of Jacobi-Trudi type for the rational solutions of the Painlevé III (PIII) equation is presented. Entries of determinant are given by the Laguerre polynomials. Degeneration of this determinant expression to that for the rational solutions of PII is discussed by applying the coalescence procedure.

AB - A determinant expression of Jacobi-Trudi type for the rational solutions of the Painlevé III (PIII) equation is presented. Entries of determinant are given by the Laguerre polynomials. Degeneration of this determinant expression to that for the rational solutions of PII is discussed by applying the coalescence procedure.

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U2 - 10.1016/S0375-9601(99)00577-0

DO - 10.1016/S0375-9601(99)00577-0

M3 - Article

AN - SCOPUS:0000268870

VL - 260

SP - 462

EP - 467

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 6

ER -