A lattice sum involving the cosine function

BOYSAL A., ECEVİT F., YILDIRIM C. Y.

Journal of Mathematical Analysis and Applications, cilt.463, sa.1, ss.134-160, 2018 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 463 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.jmaa.2018.03.014
  • Dergi Adı: Journal of Mathematical Analysis and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.134-160
  • Anahtar Kelimeler: Asymptotic approximation, Elementary classical functions, Lattice sum
  • Boğaziçi Üniversitesi Adresli: Evet

Özet

In this article we prove that, as n→∞ ∑j,k=1n−1[Formula presented] We also obtain the secondary term of size ≍n2 to be followed by an error term of size O(log⁡n). In this work, results and techniques from classical analysis involving roles by several special functions, from number theory, and from numerical analysis are needed.