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
SN - 0375-9601
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
IS - 6
ER -