7 papers
Terminating representations, transformations and summations for the and -symmetric subfamilies of the Askey--Wilson polynomials
Howard S. Cohl, Roberto S. Costas-Santos, Linus Ge
In this article, we exhaustively explore the terminating basic hypergeometric representations and transformations of the and -symmetric subfamilies of the Askey--Wilson…
The and -symmetric orthogonal polynomials in the -Askey scheme, their dual polynomials and functions, orthogonality, generating functions and relations and nonterminating -Chaundy double product representations
Howard S. Cohl, Roberto S. Costas-Santos
We derive double-product representations of nonterminating basic hypergeometric series using diagonalization, a method introduced by Theo William Chaundy in 1943. We refer to this…
The Laguerre constellation of classical orthogonal Polynomials
Roberto S. Costas-Santos
A linear functional is classical if there exist polynomials, and , with , , such that , whe…
Investigating Multidimensional Degenerate Hybrid Special Polynomials and Their Connection to Appell Sequences: Properties and Applications
Awatif Muflih Alqahtani, Saleem Yousuf, Shahid Ahmad Wani +1
This paper explores the operational principles and monomiality principle that significantly shape the development of various special polynomial families. We argue that applying the…
Asymptotics, orthogonality relations and duality for the and -symmetric polynomials in the -Askey scheme
Howard S. Cohl, Roberto S. Costas-Santos, Xiang-Sheng Wang
In this survey we summarize the current state of known orthogonality relations for the and -symmetric and dual subfamilies of the Askey--Wilson polynomials in the -A…
On Polar Jacobi Polynomials
Roberto S. Costas-Santos
In the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete-continuous Sobolev-type inner product def…