Skip navigation
Skip navigation

A Conjectured Integer Sequence Arising From the Exponential Integral

Brent, Richard; Glasser, M. L.; Guttmann, Anthony J

Description

Let f0(z)=exp(z/(1−z)), f1(z)=exp(1/(1−z))E1(1/(1−z)), where E1(x)=∫∞xe−tt−1dt. Let an=[zn]f0(z) and bn=[zn]f1(z) be the corresponding Maclaurin series coefficients. We show that an and bn may be expressed in terms of confluent hypergeometric functions. We consider the asymptotic behaviour of the sequences (an) and (bn) as n→∞, showing that they are closely related, and proving a conjecture of Bruno Salvy regarding (bn). Let ρn=anbn, so ∑ρnzn=(f0⊙f1)(z) is a Hadamard product. We obtain an...[Show more]

CollectionsANU Research Publications
Date published: 2019
Type: Journal article
URI: http://hdl.handle.net/1885/281430
Source: Journal of Integer Sequences
Access Rights: Free Access via publisher website

Download

File Description SizeFormat Image
brent21.pdf209.54 kBAdobe PDF    Request a copy


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  17 November 2022/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator