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The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis. (English) Zbl 0990.33010
The authors find asymptotic expansions of Meixner-Pollaczek, Jacobi, Meixner, and Krawtchouk polynomials in terms of Laguerre polynomials.

MSC:
33C45Orthogonal polynomials and functions of hypergeometric type
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References:
[1] Elbert, A.; Laforgia, A.: Asymptotic formulas for ultraspherical polynomials $Pn{\lambda}(x)$ and their zeros for large values of ${\lambda}$. Proc. amer. Math. soc. 114, 371-377 (1992) · Zbl 0742.33009
[2] Godoy, E.; Ronveaux, A.; Zarzo, A.; Area, I.: On the limit relations between classical continuous and discrete orthogonal polynomials. J. comp. Appl. math. 91, 97-105 (1998) · Zbl 0934.33013
[3] R. Koekoek, R.F. Swarttouw, The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Technical University Delft. Report, 1998, pp. 98--17.
[4] J.L. López, N.M. Temme, Approximations of orthogonal polynomials in terms of Hermite polynomials, Methods Appl. Anal. 6 (1999) 131--146. · Zbl 0958.33004
[5] J.L. López, N.M. Temme, The role of Hermite Polynomials in asymptotic analysis, CWI Report MAS-R9926, in: Proceedings of the International Workshop on Special Functions, Hong Kong, June 21--25, 1999, accepted for publication.
[6] López, J. L.; Temme, N. M.: Hermite polynomials in asymptotic representations of generalized Bernoulli, Euler, Bessel, and buchholz polynomials. J. math. Anal. appl. 239, 457-477 (1999) · Zbl 0979.33004
[7] Ronveaux, A.; Zarzo, A.; Area, I.; Godoy, E.: Transverse limits in the Askey tableau. J. comp. Appl. math. 98, 327-335 (1998) · Zbl 0936.33004
[8] Temme, N. M.: Special functions: an introduction to the classical functions of mathematical physics. (1996) · Zbl 0856.33001