The Properties of Binomial Transforms for Modified (s,t)-Pell Matrix Sequence

Year 2024, Volume: 7 Issue: 3, 168 - 177, 29.09.2024

Şükran Uygun , Ozan Haklıdır

https://doi.org/10.33434/cams.1524027

Abstract

In this study, we investigate a generalization of the modified Pell sequence, which is called $(s,t)$-modified Pell sequence. By considering this sequence, we define the matrix sequence whose elements are $(s,t)$-modified Pell numbers. Furthermore, we define various binomial transforms for modified $ (s,t)$-Pell matrix sequence. Finally, we give some relationships for $(s,t)$-modified Pell matrix sequences such as Binet formulas, the generating functions, and some sum formulas.

Keywords

Binet formula, Binomial transforms, Generating function, Modified (s, t)-Pell sequence

The Properties of Binomial Transforms for Modified $(s,t)$-Pell Matrix Sequence

Abstract

In this study, we investigate a generalization of the modified Pell sequence, which is called $(s,t)$-modified Pell sequence. By considering this sequence, we define the matrix sequence whose elements are $(s,t)$-modified Pell numbers. Furthermore, we define various binomial transforms for modified $ (s,t)$-Pell matrix sequence. Finally, we give some relationships for $(s,t)$-modified Pell matrix sequences such as Binet formulas, the generating functions, and some sum formulas.

Keywords

Binet formula, Binomial transforms, Generating function, Modified (s, t)-Pell sequence

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