منابع مشابه
Invariant Sequences under Binomial Transformation
The classical binomial inversion formula states that an = Hk=o(k)(~ty^k ( ~ ®> ̂ 2,...) if and only if hn = Tl=Q(l)(-l)ak (n = 0,1,2,...). In this paper we study those sequences {an} such that Hk=0(l)(-lfak = ±an (n = 0,1? 2,...). If EJU(Z)H)*"* = <**("* °), we say that {aj is an invariant sequence. If Efc=0(*)(~l)** = -an (n>0)9 we say that {an} is an inverse invariant sequence. Throughout this...
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Abstract The Levinson–Durbin recursion is used to construct the coefficients which define the minimum mean square error predictor of a new observation for a discrete time, second-order stationary stochastic process. As the sample size varies, the coefficients determine what is called a Levinson–Durbin sequence. A generalized Levinson– Durbin sequence is also defined, and we note that binomial c...
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For a delta operator aD − bD we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case of D − 1 2D 2 we show that the corresponding Bessel–Carlitz polynomials are moments of the convolution semigroup of inverse Gaussian distributions. We also find probability distributions νt, t > 0, for which {yn(t)}, the Bessel polynomials at t, is the moment ...
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ژورنال
عنوان ژورنال: Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
سال: 2019
ISSN: 2300-133X,2081-545X
DOI: 10.2478/aupcsm-2019-0008