A Note on Two Fundamental Recursive Sequences

• Autorzy: Reza Farhadian , Rafael Jakimczuk
• Języki publikacji: EN

Abstrakty

EN

In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc. We establish some general limit formulas, where the product of the first n terms of these sequences appears. Furthermore, we prove some general limits that connect these sequences to the number e(≈ 2:71828:::).(original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical programming

PL

Matematyka; Programowanie matematyczne

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2021
• Tom: 35 (2)
• Strony: 172--183

Twórcy

autor

Reza Farhadian

• Razi University Kermanshah, Iran

autor

Rafael Jakimczuk

• Universidad Nacional de Luján Luján, Buenos Aires, República Argentina

Bibliografia

• Bicknell M., A primer on the Pell sequence and related sequences, Fibonacci Quart. 13 (1975), 345-349.
• Bilgici a G. nd Sentürk T.D., Some addition formulas for Fibonacci, Pell and Jacobsthal numbers, Ann. Math. Sil. 33 (2019), 55-65.
• Farhadian R. and Jakimczuk R., Notes on a general sequence, Ann. Math. Sil. 34 (2020), 193-202.
• Horadam A.F., Pell identities, Fibonacci Quart. 9 (1971), 245-252, 263.
• Horadam A.F. and Mahon J.M., Pell and Pell-Lucas polynomials, Fibonacci Quart. 23 (1985), 7-20.
• Koshy T., Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
• Rey Pastor J., Pi Calleja P., and Trejo C.A., Análisis Matemático, Vol. 1, Editorial Kapelusz, Buenos Aires, 1969.
• Stakhov A.P, The golden section in the measurement theory, Comput. Appl. Math. 17 (1989), 613-638.

Identyfikatory

DOI

10.2478/amsil-2021-0007