q-almost Riordan arrays

Alp Y., Baran F. Y., Kocer G., TUĞLU N.

Filomat, cilt.40, sa.8, ss.3043-3059, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 40 Sayı: 8
  • Basım Tarihi: 2026
  • Doi Numarası: 10.2298/fil2608043a
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.3043-3059
  • Anahtar Kelimeler: almost-Riordan arrays, q-analogue, Riordan arrays
  • Gazi Üniversitesi Adresli: Evet

Özet

Our focus is on examining a group of Riordan arrays in which each member is represented by a triple of power series that is called an almost-Riordan array. If we take a triple of power series that is chosen as a q-function, we identify the q-analogue of the almost-Riordan arrays called q-almost Riordan arrays. In addition, we obtain the fundamental theorem for q-almost Riordan arrays (FTqARA). For suitably chosen pairs of q-almost Riordan arrays, new formulas for the multiplication of any q-almost Riordan arrays are obtained. Finally, with the help of the FTqARA, the generating functions for some row sums of q-almost Riordan matrices are derived.