On Various Binomial Transforms of the Generalized Pell Matrix Sequences

Şükran Uygun; Ozan Haklıdır

doi:10.53570/jnt.1637087

EN

On Various Binomial Transforms of the Generalized Pell Matrix Sequences

Abstract

The main aim of this study is to apply different binomial transforms to the generalized Pell matrix sequences. We define the binomial, $s$-binomial, rising, and falling transforms for the generalized Pell matrix sequence. We establish some algebraic properties, such as the recurrent formulas, Binet formulas, generating functions, and sum formulas, for binomial transforms of the generalized Pell matrix sequences. Finally, we discuss the need for further research.

Keywords

Binomial transforms, matrix sequences, generating function, Binet formula, Pell numbers

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Şükran Uygun ^*
0000-0002-7878-2175
Türkiye

Ozan Haklıdır
0009-0005-3449-9342
Türkiye

Publication Date

March 28, 2025

Submission Date

February 11, 2025

Acceptance Date

March 27, 2025

Published in Issue

Year 2025 Number: 50

DOI

https://doi.org/10.53570/jnt.1637087

IZ

https://izlik.org/JA73NS34JW

APA

Uygun, Ş., & Haklıdır, O. (2025). On Various Binomial Transforms of the Generalized Pell Matrix Sequences. Journal of New Theory, 50, 56-67. https://doi.org/10.53570/jnt.1637087

AMA

1.Uygun Ş, Haklıdır O. On Various Binomial Transforms of the Generalized Pell Matrix Sequences. JNT. 2025;(50):56-67. doi:10.53570/jnt.1637087

Chicago

Uygun, Şükran, and Ozan Haklıdır. 2025. “On Various Binomial Transforms of the Generalized Pell Matrix Sequences”. Journal of New Theory, nos. 50: 56-67. https://doi.org/10.53570/jnt.1637087.

EndNote

Uygun Ş, Haklıdır O (March 1, 2025) On Various Binomial Transforms of the Generalized Pell Matrix Sequences. Journal of New Theory 50 56–67.

IEEE

[1]Ş. Uygun and O. Haklıdır, “On Various Binomial Transforms of the Generalized Pell Matrix Sequences”, JNT, no. 50, pp. 56–67, Mar. 2025, doi: 10.53570/jnt.1637087.

ISNAD

Uygun, Şükran - Haklıdır, Ozan. “On Various Binomial Transforms of the Generalized Pell Matrix Sequences”. Journal of New Theory. 50 (March 1, 2025): 56-67. https://doi.org/10.53570/jnt.1637087.

JAMA

1.Uygun Ş, Haklıdır O. On Various Binomial Transforms of the Generalized Pell Matrix Sequences. JNT. 2025;:56–67.

MLA

Uygun, Şükran, and Ozan Haklıdır. “On Various Binomial Transforms of the Generalized Pell Matrix Sequences”. Journal of New Theory, no. 50, Mar. 2025, pp. 56-67, doi:10.53570/jnt.1637087.

Vancouver

1.Şükran Uygun, Ozan Haklıdır. On Various Binomial Transforms of the Generalized Pell Matrix Sequences. JNT. 2025 Mar. 1;(50):56-67. doi:10.53570/jnt.1637087