8 papers
Product formulas for basic hypergeometric series by evaluations of Askey--Wilson polynomials
Howard Cohl, Michael Schlosser
Ismail and Wilson derived a generating function for Askey--Wilson polynomials which is given by a product of -Gauss (Heine) nonterminating basic hypergeometric functions. We pro…
Transformations and summations for bilateral basic hypergeometric series
Howard S. Cohl, Michael J. Schlosser
We review and derive transformation and summation formulas for bilateral basic hypergeometric series. Our study focuses on consequences of certain bilateral extensions of two impor…
Connection formulas for Askey--Wilson polynomials and related expansions
Howard S. Cohl, Wolter Groenevelt
We derive and study expansions of and over the Askey--Wilson polynomials. We study these expansions and examine some limits to the continuous dual -Hahn, Al-Salam--Chihara, cont…
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…
Integral representation for a product of two Jacobi functions of the second kind
Howard S. Cohl, Loyal Durand
By starting with Durand's double integral representation for a product of two Jacobi functions of the second kind, we derive an integral representation for a product of two Jacobi…
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…