Biorthogonality and para-orthogonality of $R_I$ polynomials

Abstract

In this paper, a sequence of linear combination of $R_I$ type polynomials such that the terms in this sequence have a common zero is constructed. A biorthogonality relation arising from such a sequence is discussed. Besides a sequence of para-orthogonal polynomials by removing the common zero using suitable conditions is obtained. Finally, a case of hypergeometric functions is studied to illustrate the results obtained.

16 pages, 2 figures