Remarks on Homogeneous Al-Salam and Carlitz Polynomials
نویسندگان
چکیده
منابع مشابه
An Operator Approach to the Al-Salam-Carlitz Polynomials
We present an operator approach to Rogers-type formulas and Mehler’s formulas for the Al-Salam-Carlitz polynomials Un(x, y, a; q). By using the q-exponential operator, we obtain a Rogers-type formula which leads to a linearization formula. With the aid of a bivariate augmentation operator, we get a simple derivation of Mehler’s formula due to AlSalam and Carlitz. By means of the Cauchy companio...
متن کاملSUSLOV: The q-harmonic oscillator and the Al-Salam and Carlitz polynomials
One more model of a q-harmonic oscillator based on the q-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form of q-creation and q-annihilation operators, q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.
متن کامل5 J un 1 99 7 Multivariable Al - Salam & Carlitz polynomials associated with the type A q - Dunkl kernel
The Al-Salam & Carlitz polynomials are q-generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving a multivariable hypergeometric function which is the q-analogue of the type-A Dunkl integral kernel. An eigenoperator is established for these polynomials and this is used to prove orthogonality with ...
متن کاملJu n 19 97 Multivariable Al - Salam & Carlitz polynomials associated with the type A q - Dunkl kernel
The Al-Salam & Carlitz polynomials are q-generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving a multivariable hypergeometric function which is the q-analogue of the type-A Dunkl integral kernel. An eigenoperator is established for these polynomials and this is used to prove orthogonality with ...
متن کاملThe Andrews-Stanley partition function and Al-Salam-Chihara polynomials
We show that the generating function ∑ ω(λ) where ω(λ) denotes the four parameter weight ω(λ) = a ∑ i≥12i−1b ∑ i≥12i−1c ∑ i≥12id ∑ i≥12i, and the sum runs over all ordinary or strict partitions λ with parts each ≤ N , is expressed by the Al-Salam Chihara polynomials. As a corollary we prove C. Boulet’s results when λ runs over all ordinary or strict partitions. In the last section we study the ...
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: Journal of Mathematics
سال: 2014
ISSN: 2314-4629,2314-4785
DOI: 10.1155/2014/523013