Publication:
On Infinitely Many Rational Approximants to ζ(3)

Loading...
Thumbnail Image
Identifiers
Publication date
2019-12-03
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
MDPI AG.
Impact
Google Scholar
Export
Research Projects
Organizational Units
Journal Issue
Abstract
A set of second order holonomic difference equations was deduced from a set of simultaneous rational approximation problems. Some orthogonal forms involved in the approximation were used to compute the Casorati determinants for its linearly independent solutions. These solutions constitute the numerator and denominator sequences of rational approximants to ζ(3) . A correspondence from the set of parameters involved in the holonomic difference equation to the set of holonomic bi-sequences formed by these numerators and denominators appears. Infinitely many rational approximants can be generated.
Description
Keywords
Holonomic Difference Equation, Integer Sequences, Irrationality, Multiple Orthogonal Polynomials, Orthogonal Forms, Recurrence Relation, Simultaneous Rational Approximation
Bibliographic citation
Arvesú, J., & Soria-Lorente, A. (2019). On Infinitely Many Rational Approximants to ζ(3). In Mathematics (Vol. 7, Issue 12, p. 1176). MDPI AG.