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Lattice Paths and Positive Trigonometric Sums

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Constructive Approximation Aims and scope

Abstract.

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.

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Authors and Affiliations

  1. Department of Mathematics , University of South Florida Tampa FL 33620 USA, US

    M. E. H. Ismail

  2. Department of Mathematics KAIST Taejon 305-701 Korea, KR

    D. Kim

  3. School of Mathematics USA, University of Minnesota Minneapolis MN 55455, US

    D. Stanton

Authors
  1. M. E. H. Ismail
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  2. D. Kim
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  3. D. Stanton
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Additional information

January 22, 1997. Date revised: July 9, 1997.

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Ismail, M., Kim, D. & Stanton, D. Lattice Paths and Positive Trigonometric Sums. Constr. Approx. 15, 69–81 (1999). https://doi.org/10.1007/s003659900097

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  • DOI: https://doi.org/10.1007/s003659900097

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