On the Orthogonality of Partial Sums of Generalized Hypergeometric Series

On orthogonal Laurent polynomials related to the partial sums of power series

“…In [13] it was shown that polynomials {F n (z)} ∞ n=0 satisfy relations (8),( 9) with a n ≡ 0, and (15)…”

“…The partial sums of a power series and orthogonal Laurent polynomials. Consider a power series f (z), as in (13), its partial sums f n (z), and the associated Laurent polynomials {R k } ∞ k=0 from (16). There are various methods for deriving candidates for generating functions, as described in details in a book of McBride [8], see also a book of Rainville [9].…”

“…Theorem 1. Let f (z) be a power series from (13) with a non-zero radius of convergence ρ (≤ +∞), and f n (z) be its n-th partial sum. Let {R k (z)} ∞ k=0 be defined by (16).…”