Derivatives of Integrating Functions for Orthonormal Polynomials with Exponential-Type Weights

Let [inline-graphic not available: see fulltext], [inline-graphic not available: see fulltext], where [inline-graphic not available: see fulltext] is an even function. In 2008 we have a relation of the orthonormal polynomial [inline-graphic not available: see fulltext] with respect to the weight [inline-graphic not available: see fulltext]; [inline-graphic not available: see fulltext], where [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext] are some integrating functions for orthonormal polynomials [inline-graphic not available: see fulltext]. In this paper, we get estimates of the higher derivatives of [inline-graphic not available: see fulltext] and [inline-graphic not available: see fulltext], which are important for estimates of the higher derivatives of [inline-graphic not available: see fulltext].