関西可積分系セミナー (2004年10月19日)
- 日時
- 2004年10月19日（火）15時-16時15分
- 場所
- 京都大学本部キャンパス工学部総合校舎４０６セミナー室
高田智広 (京都大学理学部数学科)
The Mehler-Heine type formula for a certain class of 2-orthogonal polynomials of type II
The Mehler-Heine type formula tells a scaling asymptotic property of orthogonal polynomials near the endpoints of the interval of orthogonality. Certain "classical" 2-orthogonal polynomials have the same property, which can be proved by a direct calculation. Purely diagonal 2-orthogonal polynomials have four-terms recurrence formulas. We can consider the recurrence formula of the 2-orthogonal polynomials as a discretization of the Bessel equation. Thus we can prove the Mehler-Heine type formula for the broader class of 2-orthogonal polynomials.