FINITE SUMS INVOLVING TRIGONOMETRIC FUNCTIONS AND SPECIAL POLYNOMIALS: ANALYSIS OF GENERATING FUNCTIONS AND p-ADIC INTEGRALS

Kilar N., Bayad A., ŞİMŞEK Y.

Applicable Analysis and Discrete Mathematics, cilt.18, sa.2, ss.452-476, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.2298/aadm230515010k
  • Dergi Adı: Applicable Analysis and Discrete Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.452-476
  • Anahtar Kelimeler: Bernoulli and Euler numbers and polynomials, Combinatorial numbers and sums, p-adic integrals, Special functions, Stirling numbers
  • Akdeniz Üniversitesi Adresli: Evet

Özet

By using trigonometric and generating functions, some formulas and relations involving sums of powers of consecutive positive integers and certain combinatorial sums are derived. By applying the derivative operator to some certain families of special functions and finite sums involving trigonometric functions, many novel relations related to the special numbers and polynomials are obtained. Moreover, by applying p-adic integrals to these finite sums, some p-adic integral representations of trigonometric functions are found.