English

Generating Function Associated with the Rational Solutions of the Painlev\'e II Equation

Exactly Solvable and Integrable Systems 2009-11-07 v1

Abstract

We consider the Hankel determinant representation for the rational solutions of the Painlev\'e II equation. We give an explicit formula for the generating function of the entries in terms of logarithmic derivative of the Airy function, which by itself is a particular solution of the Painlev\'e II equation.

Cite

@article{arxiv.nlin/0112043,
  title  = {Generating Function Associated with the Rational Solutions of the Painlev\'e II Equation},
  author = {Katsunori Iwasaki and Kenji Kajiwara and Toshiya Nakamura},
  journal= {arXiv preprint arXiv:nlin/0112043},
  year   = {2009}
}

Comments

7 pages

R2 v1 2026-07-22T18:08:57.457Z