On new rational approximants to \zeta(3)
J. Arves\'u, A. Soria-Lorente
TL;DR
This paper introduces new rational approximants to (3) that demonstrate its irrationality, providing recurrence relations, continued fraction expansions, and comparisons with Ape9ry's approximants.
Contribution
It presents novel infinitely many rational approximants to (3), including their recurrence relations and continued fractions, expanding on Ape9ry's classical approach.
Findings
New rational approximants to (3) are constructed.
Recurrence relations and continued fractions for these approximants are derived.
Comparison shows differences and similarities with Ape9ry's approximants.
Abstract
New (infinitely many) rational approximants to \zeta(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A comparison of our approximants with Ap\'ery's approximants to \zeta(3) is shown.
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Taxonomy
TopicsMathematical functions and polynomials · Iterative Methods for Nonlinear Equations · Approximation Theory and Sequence Spaces