Generalized Stirling Numbers, Exponential Riordan Arrays, and Toda Chain Equations
School of Science
Waterford Institute of Technology
We study the properties of three families of exponential Riordan arrays
related to the Stirling numbers of the first and second kind. We relate
these exponential Riordan arrays to the coefficients of families of
orthogonal polynomials. We calculate the Hankel transforms of the
moments of these orthogonal polynomials. We show that the Jacobi
coefficients of two of the matrices studied satisfy generalized Toda
chain equations. We finish by defining and characterizing the elements
of an exponential Riordan array associated to generalized Stirling
numbers studied by Lang.
Full version: pdf,
(Concerned with sequences
Received July 16 2013; revised versions received October 1 2013; October 14 2013; December 4 2013.
Published in Journal of Integer Sequences, January 4 2014.
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