Lattice paths and positive trigonometric sums

Authors
Ismail, MEH Kim, D Stanton, D
Citation
Meh. Ismail et al., Lattice paths and positive trigonometric sums, CONSTR APPR, 15(1), 1999, pp. 69-81
Citations number
13
Categorie Soggetti
Mathematics
Journal title
CONSTRUCTIVE APPROXIMATION
ISSN journal
01764276 → ACNP
Volume
15
Issue
1
Year of publication
1999
Pages
69 - 81
Database
ISI
SICI code
0176-4276(1999)15:1<69:LPAPTS>2.0.ZU;2-J
Abstract
A trigonometric polynomial generalization to the positivity of an alternati ng sum of binomial coefficients is given. The proof uses lattice paths, and identifies the trigonometric sum as a polynomial with positive integer coe fficients. Some special cases of the q-analogue conjectured by Bressoud are established, and new conjectures are given.