CrossRef 2025 4 sitasi

A note on Fibonacci-Hermite polynomials

Ugur Duran Mehmet Acikgoz

Abstrak

We first review and analyze the golden integral and its definitions and some properties. Then we introduce a new generalization of the Hermite polynomials via the golden exponential function (called Fibonacci-Hermite polynomials) and investigate several properties and relations. We derive some explicit and implicit summation formulas for mentioned polynomials. Then, we analyze derivative properties and provide a higher-order difference equation of the Fibonacci-Hermite polynomials. Moreover, we examine a recurrence relation and integral representation. In addition, we obtain some properties of Fibonacci-Bernstein polynomials. Lastly, we obtain a correlation between the Fibonacci-Hermite polynomials and the Fibonacci-Bernstein polynomials

Penulis (2)

Ugur Duran

Mehmet Acikgoz

Format Sitasi

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Duran, U., Acikgoz, M. (2025). A note on Fibonacci-Hermite polynomials. https://doi.org/10.2298/pim2531091d

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Total Sitasi: 4×
Sumber Database: CrossRef
DOI: 10.2298/pim2531091d
Akses: Terbatas