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An exactly solvable self-convolutive recurrence

Martin, RJ and Kearney, MJ (2010) An exactly solvable self-convolutive recurrence AEQUATIONES MATH, 80 (3). 291 - 318. ISSN 0001-9054

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Abstract

We consider a self-convolutive recurrence whose solution is the sequence of coefficients in the asymptotic expansion of the logarithmic derivative of the confluent hypergeometic function U(a, b, z). By application of the Hilbert transform we convert this expression into an explicit, non-recursive solution in which the nth coefficient is expressed as the (n − 1)th moment of a measure, and also as the trace of the (n − 1)th iterate of a linear operator. Applications of these sequences, and hence of the explicit solution provided, are found in quantum field theory as the number of Feynman diagrams of a certain type and order, in Brownian motion theory, and in combinatorics.

Item Type: Article
Additional Information: The original publication is available at <a href="http://www.springerlink.com/content/p86182154qg15321/"</a>
Uncontrolled Keywords: MATRICES
Divisions: Faculty of Engineering and Physical Sciences > Electronic Engineering > Advanced Technology Institute
Depositing User: Symplectic Elements
Date Deposited: 08 Mar 2012 16:11
Last Modified: 23 Sep 2013 19:12
URI: http://epubs.surrey.ac.uk/id/eprint/205777

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