scholarly journals New examples of Krall–Meixner and Krall–Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre polynomials

2021 ◽  
pp. 105683
Author(s):  
Antonio J. Durán
Keyword(s):  
Laguerre Polynomials ◽  
Hahn Polynomials

Extended State Space of the Rational sl(2) Gaudin Model in Terms of Laguerre Polynomials

2013 ◽  
Vol 58 (11) ◽  
pp. 1084-1091
Author(s):  
Yu.V. Bezvershenko ◽  
◽  
P.I. Holod ◽  
Keyword(s):  
State Space ◽  
Laguerre Polynomials ◽  
Gaudin Model ◽  
Extended State

scholarly journals Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(α), verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

scholarly journals A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange–Hermite Polynomials

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 648
Author(s):  
Ghulam Muhiuddin ◽  
Waseem Ahmad Khan ◽  
Ugur Duran ◽  
Deena Al-Kadi
Keyword(s):  
Generating Function ◽  
Functional Equations ◽  
Laguerre Polynomials ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
New Class

The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange–Hermite polynomials. Using the generating function and their functional equations, we investigate some properties of these polynomials. Moreover, we derive several connected formulas and relations including the Miller–Lee polynomials, the Laguerre polynomials, and the Lagrange Hermite–Miller–Lee polynomials.

Identification of linear distributed systems via Laguerre polynomials

1984 ◽  
Vol 15 (10) ◽  
pp. 1101-1106 ◽  
Author(s):  
V. RANGANATHAN ◽  
A. N. JHA ◽  
V. S. RAJAMANI
Keyword(s):  
Distributed Systems ◽  
Laguerre Polynomials

Parameter estimation of discrete systems via Hahn polynomials

1987 ◽  
Vol 46 (5) ◽  
pp. 1605-1619 ◽  
Author(s):  
CHYI HWANG ◽  
CHYI-TSONG CHEN ◽  
YEN-PING SHIH
Keyword(s):  
Parameter Estimation ◽  
Discrete Systems ◽  
Hahn Polynomials
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