A Generalization of $p$-Adic Factorial

Abstract

In this paper, we establish a new approach of the p-adic analogue of Roman factorial, called p-adic Roman factorial. We define this new concept and demonstrate its properties and some properties of p-adic factorial.

Keywords

• - Roman factorial
• p-Adic factorial
• p-Adic gamma function
• p-Adic Number

References

1. S. Roman, The Logarithmic Binomial Formula. The American Mathematical Monthly 99 (7) (1992) 641-648.
2. D. E. Loeb, G. C. Rota, Formal Power Series of Logarithmic Type. Advances in Mathematics 75 (1) (1989) 1-118.
3. D. E. Loeb, A Generalization of the Binomial Coefficients. Discrete Mathematics 105 (1-3) (1992) 143-156.
4. A. M. Robert, A Course in p-Adic Analysis, Springer-Verlag, Graduate Texts in Mathematics 198, 2000.
5. H. Menken, Ö. Çolakoğlu, Some Properties of the p-Adic Beta Function. European Journal of Pure and Applied Mathematics 8 (2) (2015) 214-231.
6. R. R. Aidagulov, M. A. Alekseyev, On p-adic Approximation of Sums of Binomial Coefficients. Journal of Mathematical Sciences 233 (5) (2018) 626-634.
7. D. Knuth, Subspaces, Subsets, and Partitions. Journal of Combinatorial Theory 10 (2) (1971) 178-180.
8. U. Duran, M. Açıkgöz, A study on Novel Extensions for the p-Adic Gamma and p-Adic Beta Functions. Mathematical and Computational Applications 24 (2) (2019) 1-20.

9. U. Duran, M. Açkgöz, On p-Adic Gamma Function Related to q-Daehee Polynomials and Numbers. Proyecciones (Antofagasta), 38 (4) (2019) 799-810.
10. Ö. H. Çolakoğlu, H. Menken, On the p-Adic Gamma Function and Changhee Polynomials. Turkish Journal of Analysis and Number Theory 6 (4) (2018) 120-123.
11. Y. A. Morita, A p-Adic Analogue of the Gamma Function. Journal of the Faculty of Science, The University of Tokyo, Section 1A 22 (2) (1975) 255-266.