论文信息 - Asymptotics of Orthogonal Polynomials via Recurrence Relations

Asymptotics of Orthogonal Polynomials via Recurrence Relations

We use the Legendre polynomials and the Hermite polynomials as two examples to illustrate a simple and systematic technique on deriving asymptotic formulas for orthogonal polynomials via recurrence relations. Another application of this technique is to provide a solution to a problem recently raised by M. E. H. Ismail.

X.-S. Wang | R. Wong | Xiang-Sheng Wang

[1] Irene A. Stegun,et al. Handbook of Mathematical Functions. , 1966 .

[2] F. Olver. Asymptotics and Special Functions , 1974 .

[3] H. Li,et al. Asymptotic expansions for second-order linear difference equations , 1992 .

[4] Rene F. Swarttouw,et al. The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue Report Fac , 1996, math/9602214.

[5] Stephanos Venakides,et al. Strong asymptotics of orthogonal polynomials with respect to exponential weights , 1999 .

[6] Stephanos Venakides,et al. UNIFORM ASYMPTOTICS FOR POLYNOMIALS ORTHOGONAL WITH RESPECT TO VARYING EXPONENTIAL WEIGHTS AND APPLICATIONS TO UNIVERSALITY QUESTIONS IN RANDOM MATRIX THEORY , 1999 .

[7] Roderick Wong,et al. Asymptotic approximations of integrals , 1989, Classics in applied mathematics.

[8] Z. Wang,et al. Uniform asymptotic expansion of $J_\nu(\nu a)$ via a difference equation , 2002, Numerische Mathematik.

[9] Charles A. Micchelli,et al. Uncertainty Principles in Hilbert Spaces , 2002 .