Factorial Approach in the Real Field

Authors

  • Zaidulkhair Hamzi Universitas Negeri Makassar
  • Syamsuddin Mas'ud Universitas Negeri Makassar

DOI:

https://doi.org/10.24252/msa.v13i1.56025

Keywords:

faktorial, bidang riil, representasi integral, fungsi gamma, pendekatan analitis

Abstract

Artikel ini adalah studi literatur tentang mendefinisikan faktorial dalam domain nyata. Tujuan penelitian ini adalah untuk menurunkan rumus aproksimasi faktorial yang dinyatakan sebagai  dengan menggunakan pendekatan analitis. Makalah ini diawali dengan asumsi bahwa rumus faktorial rekursif tetap berlaku pada domain riil, kemudian digunakan untuk mengkonstruksi rumus aproksimasi . Selanjutnya, makalah ini juga mengaitkan hasil dari bentuk aproksimasi faktorial dengan representasi integral yang relevan, seperti fungsi gamma.

References

J. Pitman, “Probability,” 1993, doi: 10.1007/978-1-4612-4374-8.

F. Cajori, “A history of mathematical notations: Two volumes bound as one,” Differ. Equations, 1928, Accessed: Mar. 10, 2025. [Online]. Available: https://books.google.com/books/about/A_History_of_Mathematical_Notations.html?hl=id&id=7juWmvQSTvwC

A. D. D. Craik, “Prehistory of Faà di Bruno’s Formula,” Am. Math. Mon., vol. 112, no. 2, pp. 119–130, 2005, doi: 10.1080/00029890.2005.11920176.

P. J. Davis, “Leonhard Euler’s Integral: A Historical Profile of the Gamma Function,” Am. Math. Mon., vol. 66, no. 10, pp. 849–869, 1959, doi: 10.1080/00029890.1959.11989422.

J. M. Borwein and R. M. Corless, “Gamma and Factorial in the Monthly,” Am. Math. Mon., vol. 125, no. 5, pp. 400–424, 2018, doi: 10.1080/00029890.2018.1420983.

[6] C. P. Nicholas and R. C. Yates, “The Probability Integral,” Am. Math. Mon., vol. 57, no. 6, p. 412, 1990, doi: 10.2307/2307644.

K. Conrad, “the Gaussian Integral,” Math.Uconn.Edu, vol. c, pp. 1–11, 2016, [Online]. Available: http://www.math.uconn.edu/~kconrad/blurbs/analysis/gaussianintegral.pdf

E. D. Bloch, “The Real Numbers and Real Analysis,” Real Numbers Real Anal., 2011, doi: 10.1007/978-0-387-72177-4.

K. A. . Ross, “Elementary analysis : the theory of calculus,” p. 351, 2003.

P. Giblin, “The Mathematical Gazette,” Mathematical Assosiation, 1972, pp. 274–284. doi: 10.1038/139163a0.

[11] T. M. Apostol, “Mathematical Analysis, Second Edition,” Education, vol. 9, no. 3, p. 492, 1974.

[12] “Concrete Mathematics: A Foundation for Computer Science - Ronald L. Graham, Donald E. Knuth, Oren Patashnik - Google Buku.” https://books.google.co.id/books/about/Concrete_Mathematics.html?id=ctnPEAAAQBAJ&redir_esc=y (accessed Mar. 10, 2025).

J. D. Hamkins, “Proof and the art of mathematics,” Proof Prog. Math., vol. 111, no. 2, p. 208, 2020, Accessed: Mar. 10, 2025. [Online]. Available: https://books.google.com/books/about/Proof_and_the_Art_of_Mathematics.html?hl=id&id=EVX6DwAAQBAJ

D. Salwinski, “Euler’s Sine Product Formula: An Elementary Proof,” Coll. Math. J., vol. 49, no. 2, pp. 126–135, 2018, doi: 10.1080/07468342.2018.1419703.

Published

2025-06-03

How to Cite

[1]
Zaidulkhair Hamzi and Syamsuddin Mas’ud, “Factorial Approach in the Real Field”, MSA, vol. 13, no. 1, pp. 69–75, Jun. 2025.