Studying some applications of the Lambert  function in elementary mathematics

Duc Thinh Vo1, Phuong Nam Bui2,
1 Faculty of Mathematics and Informatics Education, School of Education, Dong Thap University, Cao Lanh 870000, Vietnam
2 Student, Faculty of Mathematics and Informatics Education, School of Education, Dong Thap University, Cao Lanh 870000, Vietnam

Main Article Content

Abstract

This paper first introduces the Lambert  function and discuss some of its fundamental properties. Next, it establishes a process for computing or approximating the value of the Lambert  function at a given point. Furthermore, it presents several applications of the Lambert  function in constructing and solving problems in elementary mathematics, including solving exponential equations and determining the limits of sequences. Finally, a collection of illustrative problems are provided to demonstrate these applications.

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References

Beardon, A. F. (2021). The principal branch of the Lambert W function. Computational Methods and Function Theory, 21(2), 307-316. https://doi.org/10.1007/s40315-020-00329-6.
Corless, R. M., Gonnet, G. H., Hare, D. E., Jeffrey, D. J., & Knuth, D. E. (1996). On the Lambert W function. Advances in Computational mathematics, 5, 329-359. https://doi.org/10.1007/BF02124750.
Euler, L. (1783). De serie Lambertina Plurimisque eius insignibus proprietatibus. Acta Academiae scientiarum imperialis petropolitanae, 29-51.
Hoàng, V. A., & Nguyễn, T. H. L. (2023). Ứng dụng của hàm Lambert W đối với một dạng phương trình, hệ phương trình vi phân có trễ. Tạp chí Khoa học - Đại học Tây Bắc, (28), 54-58. https://tapchi.utb.edu.vn/index.php/journalofscience/article/view/446/510.
Hoorfar, A., & Hassani, M. (2008). Inequalities on the Lambert W function and hyperpower function. Journal of Inequalities in Pure and Applied Mathematics, 9(2), 5-9. https://eudml.org/doc/130024.
Iacono, R., & Boyd, J. P. (2017). New approximations to the principal real-valued branch of the Lambert W-function. Advances in Computational Mathematics, 43, 1403-1436. https://doi.org/10.1007/s10444-017-9524-6.
Lambert, J. H. (1758). Observationes variae in mathesin puram. Acta Helvetica, 3(1), 128-168.
Lehtonen, J. (2016). The Lambert W function in ecological and evolutionary models. Methods in Ecology and Evolution, 7(9), 1110-1118. https://doi.org/10.1111/2041-210X.12558
Mező, I. (2022). The Lambert W function: its generalizations and applications. Chapman and Hall/CRC.
Phan, S. (2020). Hàm Lambert W và ứng dụng để biểu diễn nghiệm của phương trình. MATH√N.COM. https://www.mathvn.com/2020/08/ham-lambert-w-va-ung-dung-e-bieu-dien.html.

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