Constructive Approximation

, Volume 15, Issue 1, pp 69–81

Lattice Paths and Positive Trigonometric Sums

  • M. E. H. Ismail
  • D. Kim
  • D. Stanton

DOI: 10.1007/s003659900097

Cite this article as:
Ismail, M., Kim, D. & Stanton, D. Constr. Approx. (1999) 15: 69. doi:10.1007/s003659900097


A trigonometric polynomial generalization to the positivity of an alternating sum of binomial coefficients is given. The proof uses lattice paths, and identifies the trigonometric sum as a polynomial with positive integer coefficients. Some special cases of the q -analogue conjectured by Bressoud are established, and new conjectures are given.

Key words. Lattice paths, Binomial coefficients, Quadrature, Positivity. AMS Classification. Primary: 42A32; Secondary: 05C38.

Copyright information

©  Springer-Verlag New York 1999

Authors and Affiliations

  • M. E. H. Ismail
    • 1
  • D. Kim
    • 2
  • D. Stanton
    • 3
  1. 1.Department of Mathematics US
  2. 2.Department of Mathematics KAIST Taejon 305-701 KoreaKR
  3. 3.School of Mathematics USAUS