A Generalization of p-Adic Factorial

A Generalization of p-Adic Factorial

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.

___

  • [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, ̈O. C ̧ olako ̆glu, 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. A ̧cıkg ̈oz, 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. A ̧cıkg ̈oz, On p-Ddic Gamma Function Related to q-Daehee Polynomials and Num- bers. Proyecciones (Antofagasta) 38 (4) (2019) 799–810.
  • [10] ̈O. H. C ̧ olako ̆glu, 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.