General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints
نویسندگان
چکیده
منابع مشابه
Matrix approach to Appell polynomials
In the last years the Appell polynomials, named after Paul Émile Appell which introduced them in 1880 [1], have gained renewed interest and has been studied by several authors. In particular, some new characterizations of Appell polynomials themselves through new approaches have been considered. To quote some of them we mention, for instance, the novel approach developed in [5], which makes use...
متن کاملAlgebraic Theory of Appell Polynomials with Application to General Linear Interpolation Problem
Sequences of polynomials, verifying the (▭), nowadays called Appell polynomials, have been well studied because of their remarkable applications not only in different branches of mathematics ([2], [3]) but also in theoretical physics and chemistry ([4], [5]). In 1936 an initial bibliography was provided by Davis (p. 25[6]). In 1939 Sheffer ([7]) introduced a new class of polynomials which exten...
متن کاملAppell Polynomials and Their Relatives
This paper summarizes some known results about Appell polynomials and investigates their various analogs. The primary of these are the free Appell polynomials. In the multivariate case, they can be considered as natural analogs of the Appell polynomials when polynomials in noncommuting variables are considered. They also fit well into the framework of free probability. For the free Appell polyn...
متن کاملLimit Theorems for Bivariate Appell
Consider the stationary linear process X t = P 1 u=?1 a(t?u) u , t 2 Z, where f u g is an i.i.d. nite variance sequence. The spectral density of fX t g may diverge at the origin (long-range dependence) or at any other frequency. Consider now the quadratic form Q N = P N t;s=1 b(t ? s)P m;n (X t ; X s), where P n;m (X t ; X s) denotes a non-linear function (Appell polynomial). We provide general...
متن کاملOn Multiple Appell Polynomials
In this paper, we first define the multiple Appell polynomials and find several equivalent conditions for this class of polynomials. Then we give a characterization theorem that if multiple Appell polynomials are also multiple orthogonal, then they are the multiple Hermite polynomials.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2021
ISSN: 2227-7390
DOI: 10.3390/math9090964