Uniform asymptotic expansions of the Tricomi-Carlitz polynomials

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • Kei Fung LEE
  • R. Wong

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)2513-2519
Journal / PublicationProceedings of the American Mathematical Society
Volume138
Issue number7
Publication statusPublished - Jul 2010

Abstract

The Tricomi-Carlitz polynomials satisfy the second-order linear difference equation (n + 1)fn+1 (α) (x) - (n + α)x f n (α) (x) + fn-1 (α) (x) = 0, n≥ 1, with initial values f0 (α) (x) = 1 and f1 (α) (x) = αx, where x is a real variable and α is a positive parameter. An asymptotic expansion is derived for these polynomials by using the turning-point theory for three-term recurrence relations developed by Wang and Wong [Numer. Math. 91(2002) and 94(2003)]. The result holds uniformly in regions containing the critical values x = ±2/√v , here ? = n + 2α - 1/2. © 2010 American Mathematical Society.

Research Area(s)

  • Difference equation, Tricomi-Carlitz polynomials, Uniform asymptotic expansion

Citation Format(s)

Uniform asymptotic expansions of the Tricomi-Carlitz polynomials. / LEE, Kei Fung; Wong, R.
In: Proceedings of the American Mathematical Society, Vol. 138, No. 7, 07.2010, p. 2513-2519.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review