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...
متن کاملUltraspherical Type Generating Functions for Orthogonal Polynomials
We characterize, up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. 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 positivity condit...
متن کاملUltraspherical Type Generating Functions for Orthogonal Polynomials
We characterize, under some technical assumptions and up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. Our method is based on differential equations and the obtained measures are particular Beta distributions. We actually recover the free Meixner family of probability distributions so that our met...
متن کاملDesign of Nonrecursive Digital Filters Using the Ultraspherical Window Function
An efficient method for the design of nonrecursive digital filters using the ultraspherical window function is proposed. Economies in computation are achieved in two ways. First, through an efficient formulation of the window coefficients, the amount of computation required is reduced to a small fraction of that required by standard methods. Second, the filter length and the independent window ...
متن کاملDesign of the Ultraspherical Window Function and Its Applications
Window functions are used to reduce Gibbs’ oscillations resulting from the truncation of a Fourier series and they are employed in a variety of signal processing applications including power spectral estimation, beamforming, and digital filter design. In this dissertation, the application of window functions based on the ultraspherical window is explored. First, two methods for evaluating the c...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1957
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1957.7.1319