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A Conjectured Integer Sequence Arising From the Exponential Integral

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


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
Source: Journal of Integer Sequences
Access Rights: Free Access via publisher website


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