• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Working paper

Orthorecursive expansion of unity

arxiv.org. math. Cornell University, 2019. No. 1901.04004.
Kalmynin A. B., Косенко П. Р.
We study the properties of a sequence c_n defined by the recursive relation c_0/(n+1)+c_1/(n+2)+…+c_n/(2n+1)=0 for n>1 and c_0=1. This sequence also has an alternative definition in terms of certain norm minimization in the space L^2([0,1]). We prove estimates on growth order of c_n and the sequence of its partial sums, infinite series identities, connecting c_n with harmonic numbers H_n and also formulate some conjectures based on numerical computations.