On the iterated binomial transforms for the generalized Mersenne polynomials

Year 2025, Volume: 74 Issue: 4, 572 - 581, 24.12.2025

Nazmiye Yılmaz

https://doi.org/10.31801/cfsuasmas.1580384

https://izlik.org/JA99SM45AC

Abstract

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.

Keywords

Binomial transform , iterated binomial transform , Mersenne polynomials , Mersenne-Lucas polynomials

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