Uniform inequalities for ultraspherical polynomials and Bessel functions of fractional order
نویسندگان
چکیده
منابع مشابه
Ultraspherical Type Generating Functions for Orthogonal Polynomials
We characterize the probability distributions of finite all order moments having generating functions for orthogonal polynomials of ultraspherical type. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positive conditions ([9]). Th...
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Let up denote the normalized, generalized Bessel function of order p which depends on two parameters b and c and let λp(x) = up(x), x ≥ 0. It is proven that under some conditions imposed on p, b, and c the Askey inequality holds true for the function λp , i.e., that λp(x) +λp(y) ≤ 1 +λp(z), where x, y ≥ 0 and z = x + y. The lower and upper bounds for the function λp are also established.
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1987
ISSN: 0021-9045
DOI: 10.1016/0021-9045(87)90072-4