Difference Equations, Special Functions and Orthogonal Polynomials

10.1142/6446 ◽  
2007 ◽  
Keyword(s):  
Orthogonal Polynomials ◽  
Difference Equations ◽  
Special Functions

scholarly journals Preface: Orthogonal polynomials, special functions, and applications

2018 ◽  
Vol 141 (4) ◽  
pp. 421-423
Author(s):  
Peter A. Clarkson ◽  
Adri B. Olde Daalhuis
Keyword(s):  
Orthogonal Polynomials ◽  
Special Functions

Special Functions and Orthogonal Polynomials

2009 ◽  
pp. 261-268
Author(s):  
Inna Shingareva ◽  
Carlos Lizárraga-Celaya
Keyword(s):  
Orthogonal Polynomials ◽  
Special Functions

scholarly journals Limiting Values and Functional and Difference Equations

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 407 ◽  
Author(s):  
N.-L. Wang ◽  
Praveen Agarwal ◽  
S. Kanemitsu
Keyword(s):  
Difference Equations ◽  
Functional Equations ◽  
Boundary Behavior ◽  
Special Functions ◽  
Asymptotic Formulas ◽  
Limit Values ◽  
Summatory Function ◽  
The Difference ◽  
Limiting Values ◽  
Mathematics And Science

Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equation is used coupled with the relevant functional equations to give rise to unexpected results. As main results, this involves the expression for the Laurent coefficients including the residue, the Kronecker limit formulas and higher order coefficients as well as the difference formed to cancel the inaccessible part, typically the Clausen functions. We establish these by the relation between bases of the Kubert space of functions. Then these expressions are equated with other expressions in terms of special functions introduced by some difference equations, giving rise to analogues of the Lerch-Chowla-Selberg formula. We also state Abelian results which not only yield asymptotic formulas for weighted summatory function from that for the original summatory function but assures the existence of the limit expression for Laurent coefficients.

scholarly journals LIE ALGEBRAIC DISCRETIZATION OF DIFFERENTIAL EQUATIONS

1995 ◽  
Vol 10 (24) ◽  
pp. 1795-1802 ◽  
Author(s):  
YURI SMIRNOV ◽  
ALEXANDER TURBINER
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Difference Equations ◽  
Heisenberg Algebra ◽  
Difference Operators ◽  
Discrete Version ◽  
Classical Orthogonal Polynomials ◽  
Finite Difference Equations ◽  
Exactly Solvable

A certain representation for the Heisenberg algebra in finite difference operators is established. The Lie algebraic procedure of discretization of differential equations with isospectral property is proposed. Using sl 2-algebra based approach, (quasi)-exactly-solvable finite difference equations are described. It is shown that the operators having the Hahn, Charlier and Meissner polynomials as the eigenfunctions are reproduced in the present approach as some particular cases. A discrete version of the classical orthogonal polynomials (like Hermite, Laguerre, Legendre and Jacobi ones) is introduced.

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