Next Article in Journal
Oscillatory Properties of Third-Order Neutral Delay Differential Equations with Noncanonical Operators
Next Article in Special Issue
A Characterization of Polynomial Density on Curves via Matrix Algebra
Previous Article in Journal
Tseng Type Methods for Inclusion and Fixed Point Problems with Applications
Previous Article in Special Issue
Robust Stability of Hurwitz Polynomials Associated with Modified Classical Weights
Open AccessArticle

On Infinitely Many Rational Approximants to ζ(3)

1
Department of Mathematics, Universidad Carlos III de Madrid, Avda de la Universidad, 30, 28911 Leganés, Spain
2
Technology Department, University of Granma, Bayamo 85100, Cuba
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1176; https://doi.org/10.3390/math7121176
Received: 3 October 2019 / Revised: 18 November 2019 / Accepted: 23 November 2019 / Published: 3 December 2019
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. View Full-Text
Keywords: holonomic difference equation; integer sequences; irrationality; multiple orthogonal polynomials; orthogonal forms; recurrence relation; simultaneous rational approximation holonomic difference equation; integer sequences; irrationality; multiple orthogonal polynomials; orthogonal forms; recurrence relation; simultaneous rational approximation
Show Figures

Figure 1

MDPI and ACS Style

Arvesú, J.; Soria-Lorente, A. On Infinitely Many Rational Approximants to ζ(3). Mathematics 2019, 7, 1176.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop