On Infinitely Many Rational Approximants to zeta(3) Articles uri icon

publication date

  • December 2019

start page

  • 1

end page

  • 16


  • 12(1176)


  • 7

International Standard Serial Number (ISSN)

  • 2227-7390


  • 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 zeta(3) . A correspondence from the set of parameters involved in the holonomic difference equation to the set of holonomic bisequences formed by these numerators and denominators appears. Infinitely many rational approximants can be generated.


  • holonomic difference equation; integer sequences; irrationality; multiple orthogonal polynomials; orthogonal forms; recurrence relation; simultaneous rational approximation