scholarly journals Some Families of Generating Functions for the Jacobi and Related Orthogonal Polynomials

1999 ◽  
Vol 238 (2) ◽  
pp. 385-417 ◽  
Author(s):  
Giovanna Pittaluga ◽  
Laura Sacripante ◽  
H.M. Srivastava
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions

SYMMETRIC FUNCTIONS OF BINARY PRODUCTS OF TRIBONACCI LUCAS NUMBERS AND ORTHOGONAL POLYNOMIALS

2021 ◽  
Vol 21 (2) ◽  
pp. 461-478
Author(s):  
HIND MERZOUK ◽  
ALI BOUSSAYOUD ◽  
MOURAD CHELGHAM
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions ◽  
Symmetric Functions ◽  
Lucas Numbers

In this paper, we will recover the new generating functions of some products of Tribonacci Lucas numbers and orthogonal polynomials. The technic used her is based on the theory of the so called symmetric functions.

scholarly journals Generating Functions for Orthogonal Polynomials of A2, C2 and G2

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 354 ◽  
Author(s):  
Tomasz Czyżycki ◽  
Jiří Hrivnák ◽  
Jiří Patera
Keyword(s):  
Orthogonal Polynomials ◽  
Lie Algebras ◽  
Chebyshev Polynomials ◽  
Generating Functions ◽  
Bell Polynomials ◽  
The Third ◽  
Weight Lattice ◽  
Hybrid Character ◽  
Polynomial Family

The generating functions of fourteen families of generalized Chebyshev polynomials related to rank two Lie algebras A 2 , C 2 and G 2 are explicitly developed. There exist two classes of the orthogonal polynomials corresponding to the symmetric and antisymmetric orbit functions of each rank two algebra. The Lie algebras G 2 and C 2 admit two additional polynomial collections arising from their hybrid character functions. The admissible shift of the weight lattice permits the construction of a further four shifted polynomial classes of C 2 and directly generalizes formation of the classical univariate Chebyshev polynomials of the third and fourth kinds. Explicit evaluating formulas for each polynomial family are derived and linked to the incomplete exponential Bell polynomials.

scholarly journals Bilinear Generating Functions for Orthogonal Polynomials

1999 ◽  
Vol 15 (4) ◽  
pp. 481-497 ◽  
Author(s):  
H. T. Koelink ◽  
J. Van der Jeugt
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions

scholarly journals Symmetric functions of binary products of fibonacci and orthogonal polynomials

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1495-1504 ◽  
Author(s):  
Ali Boussayoud ◽  
Mohamed Kerada ◽  
Serkan Araci ◽  
Mehmet Acikgoz ◽  
Ayhan Esi
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions ◽  
Symmetric Functions ◽  
Fibonacci Numbers ◽  
Chebychev Polynomials ◽  
Symmetric Properties

In this paper, we introduce a new operator in order to derive some new symmetric properties of Fibonacci numbers and Chebychev polynomials of first and second kind. By making use of the new operator defined in this paper, we give some new generating functions for Fibonacci numbers and Chebychev polynomials of first and second kinds.

scholarly journals Generating functions of binary products of k-Fibonacci and orthogonal polynomials

2019 ◽  
Vol 113 (3) ◽  
pp. 2575-2586 ◽  
Author(s):  
Ali Boussayoud ◽  
Souhila Boughaba ◽  
Mohamed Kerada ◽  
Serkan Araci ◽  
Mehmet Acikgoz
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions

On the generating functions of a random walk on the non-negative integers

1996 ◽  
Vol 33 (04) ◽  
pp. 1033-1052
Author(s):  
Holger Dette
Keyword(s):  
Random Walk ◽  
Orthogonal Polynomials ◽  
State Space ◽  
Generating Functions ◽  
Spectral Measure ◽  
Stieltjes Transform ◽  
Explicit Representations ◽  
Step Transition

In the random walk whose state space is a subset of the non-negative integers explicit representations for the generating functions of then-step transition and the first return probabilities are obtained. These representations involve the Stieltjes transform of the spectral measure of the process and the corresponding orthogonal polynomials. Several examples are given in order to illustrate the application of the results.

scholarly journals GENERATING FUNCTIONS OF CAUCHY–STIELTJES TYPE FOR ORTHOGONAL POLYNOMIALS

2009 ◽  
Vol 12 (01) ◽  
pp. 91-98 ◽  
Author(s):  
MAREK BOŻEJKO ◽  
NIZAR DEMNI
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions ◽  
Short Proof ◽  
Probabilistic Interpretation ◽  
Infinitely Divisible ◽  
The Family ◽  
Multiplicative Renormalization ◽  
Renormalization Method ◽  
Stieltjes Type

We give a free probabilistic interpretation of the multiplicative renormalization method. As a byproduct, we give a short proof of the Asai–Kubo–Kuo problem on the characterization of the family of measures for which this method applies with h(x) = (1 - x)-1 which turns out to be the free Meixner family. We also give a representation of the Voiculescu transform of all free Meixner laws (even in the non-freely infinitely divisible case).

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