Journal of Integer Sequences, Vol. 3 (2000), Article 00.2.1

Generating Functions via Hankel and Stieltjes Matrices

Paul Peart and Wen-Jin Woan
Department of Mathematics
Howard University
Washington D.C. 20059
Email address: pp@scs.howard.edu

Abstract: When the Hankel matrix formed from the sequence 1, a₁, a₂, ... has an LDL^T decomposition, we provide a constructive proof that the Stieltjes matrix S_L associated with L is tridiagonal. In the important case when L is a Riordan matrix using ordinary or exponential generating functions, we determine the specific form that S_L must have, and we demonstrate, constructively, a one-to-one correspondence between the generating function for the sequence and S_L. If L is Riordan when using ordinary generating functions, we show how to derive a recurrence relation for the sequence.

(Concerned with sequences A000108, A000166, A000957, A000984, A001003, A001850, A002426, A005773, A006318, A054912)

Received May 15, 1999; published in Journal of Integer Sequences June 4, 2000.