Uniform asymptotic expansions of the Pollaczek polynomials

作者：Zhao, YQ^*; Zhou, JR

来源：Journal of Computational and Applied Mathematics, 2006, 190(1-2): 37-56.

DOI：10.1016/j.cam.2005.01.049

• Pollaczek polynomials
• uniform asymptotic expansion
• parabolic cylinder function
• airy function

Two uniform asymptotic expansions are obtained for the Pollaczek polynomials P-n(cos theta; a, b). One is for theta epsilon (0, delta/root n], 0 < delta < root a b, in terms of elementary functions and in descending powers of root n. The other is for theta epsilon [delta/root n, pi/2], in terms of a special function closely related to the modified parabolic cylinder functions, in descending powers of n. This interval contains a turning point and all possible zeros of P-n (cos theta) in theta epsilon (0, pi/2].

• 出版日期2006-6-1
• 单位中山大学