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Evaluation of some Hankel determinants

✍ Scribed by Qing-Hu Hou; Alain Lascoux; Yan-Ping Mu


Book ID
108047072
Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
89 KB
Volume
34
Category
Article
ISSN
0196-8858

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The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval. The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.

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We use combinatorial methods to evaluate Hankel determinants for the sequence of sums of consecutive t-Motzkin numbers. More specifically, we consider the following determinant: where t is a real number and m t k is the total weight of all paths from (0, 0) to (k, 0) that stay above the x-axis and

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A procedure for the numerical evaluation of the nth-order Hankel transform is presented. It is based on an extension of the zeroth-order algorithm proposed by S. Candel. Using an integral representation of the Bessel function, a formula is derived for the transform as a weighted integral of the Four