scholarly journals Sine and cosine types of generating functions

2021 ◽  
pp. 2-2
Author(s):  
Mohammad Masjed-Jamei ◽  
Zahra Moalemi
Keyword(s):  
Orthogonal Polynomials ◽  
Generating Functions ◽  
Genocchi Numbers

We introduce two sine and cosine types of generating functions in a general case and apply them to the generating functions of classical hypergeometric orthogonal polynomials as well as some widely investigated combinatorial numbers such as Bernoulli, Euler and Genocchi numbers. This approach can also be applied to other celebrated sequences.

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 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

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 A New Class of Laguerre-based Generalized Apostol Polynomials

2016 ◽  
Vol 57 (1) ◽  
pp. 67-89 ◽  
Author(s):  
N.U. Khan ◽  
T. Usman
Keyword(s):  
Generating Functions ◽  
General Symmetry ◽  
Genocchi Numbers ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulae

Abstract In this paper, we introduce a unified family of Laguerre-based Apostol Bernoulli, Euler and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities arising from different analytical means and applying generating functions. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.

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.

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