commun. fac. sci. univ. ank. ser. a1 math. stat. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 1303-5991 2618-6470 Ankara University 10.31801/cfsuasmas.1580384 Algebra and Number Theory Cebir ve Sayı Teorisi On the iterated binomial transforms for the generalized Mersenne polynomials https://orcid.org/0000-0002-7302-2281 Yılmaz Nazmiye KARAMANOĞLU MEHMETBEY ÜNİVERSİTESİ 12 24 2025 74 4 572 581 11 07 2024 07 06 2025 Copyright © 1948, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 1948 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics

We define in this study the binomial transform for the generalized Mersenne polynomials. We additionally subject the generalized Mersenne polynomials to "$r$" times the binomial transform. Also, recurrence relations are used to find the summations, Binet formulas, and generating functions of these transforms.

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