Published April 20, 2012 | Version v1
Journal article Metadata-only

Direct ultradiscretization of Ai and Bi functions and special solutions for the Painlevé II equation

Creators

  • 1. Department of Physics and Mathematics, Aoyama Gakuin University, 5-10-1 Fuchinobe, Chuo-ku, Sagamihara-shi, Kanagawa 252-5258 (Japan)
  • 2. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914 (Japan)

Description

Ultradiscrete Ai and Bi functions are directly derived through the ultradiscrete limit from q-difference analogues of the Ai and Bi functions, respectively. An infinite number of identities among the number of restricted partitions are obtained as by-products. A direct relationship between a class of special solutions for the ultradiscrete Painlevé II equation and those of the q-Painlevé II equation which have a determinantal structure is also established. (paper)

Availability note (English)

Available from http://dx.doi.org/10.1088/1751-8113/45/15/155203

Additional details

Identifiers

DOI
10.1088/1751-8113/45/15/155203;

Publishing Information

Journal Title
Journal of Physics. A, Mathematical and Theoretical (Online)
Journal Volume
45
Journal Issue
15
Journal Page Range
[13 p.]
ISSN
1751-8121

INIS

Country of Publication
United Kingdom
Country of Input or Organization
International Atomic Energy Agency (IAEA)
INIS RN
43092829
Subject category
S97: MATHEMATICAL METHODS AND COMPUTING;
Descriptors DEI
EQUATIONS; FUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; PARTITION