Two inequalities for the associated Pollaczek polynomials

[摘要] In this paper, we prove two concise inequalities for the associated Pollaczek polynomials. The first one is obtained by using Askey’s theorem (SIAM J. Math. Anal. 2:340–346, 1971) on orthogonal expansions with positive coefficients. The second one is proved by using a triple integral representation due to the authors (Integral Transforms Spec. Funct. 30:893–919, 2019). In the concluding section, we briefly point out some useful variations and known cases of our inequalities.

[学科分类] 电力

[关键词] Inequality;Laguerre polynomial;Pollaczek polynomial