The Restricted Toda Chain, Exponential Riordan Arrays, and Hankel Transforms
نویسنده
چکیده
with u0 = 0, where the dot indicates differentiation with respect to t. In this note, we shall show how solutions to this equation can be formulated in the context of exponential Riordan arrays. The Riordan arrays we shall consider may be considered as parameterised (or “time”-dependent) Riordan arrays. We have already considered parameterized Riordan arrays [1], exploring the links between these Riordan arrays and orthogonal polynomials. The restricted Toda chain equation is closely related to orthogonal polynomials, since the functions un and bn can be considered as the coefficients in the usual three-term recurrence [4, 10, 22] satisfied by orthogonal polynomials:
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