On Infinitely Many Rational Approximants to ? (3)

Jorge Arvesú and Anier Soria-Lorente
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Jorge Arvesú: Department of Mathematics, Universidad Carlos III de Madrid, Avda de la Universidad, 30, 28911 Leganés, Spain
Anier Soria-Lorente: Technology Department, University of Granma, Bayamo 85100, Cuba

Mathematics, 2019, vol. 7, issue 12, 1-16

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.

Keywords: holonomic difference equation; integer sequences; irrationality; multiple orthogonal polynomials; orthogonal forms; recurrence relation; simultaneous rational approximation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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