Document Type
Lecture
Publication Date
10-25-2019
Abstract
First, a brief introduction along with a historical background will be presented. Then, a second-order holonomic difference equation is derived from a simultaneous rational approximation problem. Some orthogonal forms involved in this approximation problem are 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.
Relational Format
presentation
Recommended Citation
Carballo, Jorge Arvesú, "On Hermite-Padé approximation, Apéry’s theorem, and the construction of infinitely many rational approximants to ζ(3)" (2019). Analysis Seminar. 1.
https://egrove.olemiss.edu/math_analysis/1