Let introduce the Sobolev type inner productIn this paper we prove a Cohen type inequality for the Fourier expansion in terms of the orthonormal polynomials associated with the above Sobolev inner product. In particular, for M = N = 0, we extend the result of Markett [C. Markett, Cohen type inequalities for Jacobi, Laguerre and
In this paper we deal with sequences of polynomials orthogonal with respect to the discrete Sobolev inner productwhere ω is a weight function, ξ ≤ 0, and M, N ≥ 0. The location of the zeros of discrete Sobolev orthogonal polynomials is given in terms of the zeros of standard polynomials orthogonal with respect to the weight function ω. In particular, for ω(x) = x α e −x we obtain the asymptotics for discrete Laguerre-Sobolev orthogonal polynomials.
We study the maximum value of the confluent hypergeometric function with oscillatory conditions of parameters. As a consequence, we obtain new inequalities for the Gauss hypergeometric function.
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