Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner–Pollaczek polynomials

2017 ◽  
Vol 45 (1) ◽  
pp. 33-56 ◽  
Author(s):  
D. D. Tcheutia ◽  
P. Njionou Sadjang ◽  
W. Koepf ◽  
M. Foupouagnigni
Keyword(s):  
Difference Equation ◽  
Divided Difference ◽  
Pollaczek Polynomials

scholarly journals On the Polynomial Solution of Divided-Difference Equations of the Hypergeometric Type on Nonuniform Lattices

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 47 ◽  
Author(s):  
Mama Foupouagnigni ◽  
Salifou Mboutngam
Keyword(s):  
Difference Equation ◽  
Divided Difference ◽  
Polynomial Solution ◽  
Formal Proof ◽  
Second Order ◽  
Fixed Degree ◽  
Hypergeometric Type ◽  
The Mean ◽  
The Right

In this paper, we provide a formal proof of the existence of a polynomial solution of fixed degree for a second-order divided-difference equation of the hypergeometric type on non-uniform lattices, generalizing therefore previous work proving existence of the polynomial solution for second-order differential, difference or q-difference equation of hypergeometric type. This is achieved by studying the properties of the mean operator and the divided-difference operator as well as by defining explicitly, the right and the “left” inverse for the second operator. The method constructed to provide this formal proof is likely to play an important role in the characterization of orthogonal polynomials on non-uniform lattices and might also be used to provide hypergeometric representation (when it does exist) of the second solution—non polynomial solution—of a second-order divided-difference equation of hypergeometric type.

Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials

2018 ◽  
Vol 11 (3) ◽  
pp. 29-39
Author(s):  
E. I. Jafarov ◽  
A. M. Jafarova ◽  
S. M. Nagiyev
Keyword(s):  
Recurrence Relations ◽  
Pollaczek Polynomials

STABILITY AND BOUNDEDNESS PROPERTIES OF A RATIONAL EXPONENTIAL DIFFERENCE EQUATION

2020 ◽  
Vol 9 (7) ◽  
pp. 4945-4954
Author(s):  
J. Leo Amalraj ◽  
M. Maria Susai Manuel ◽  
D. S. Dilip ◽  
P. Venkata Mohan Reddy
Keyword(s):  
Difference Equation
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