The q-Integers and the Mersenne Numbers

10 Pages Posted: 11 Jun 2018

See all articles by Amelia Carolina Sparavigna

Amelia Carolina Sparavigna

Polytechnic University of Turin - Department of Applied Science and Technology

Date Written: May 23, 2018

Abstract

Here we will show that the q-integers, the q-analogue of the integers that we can find in the q-calculus, are forming an additive group having a generalized sum similar to the sum of the Tsallis q-entropies of independent systems. The symmetric form of q-integers will be studied too. We will see that these numbers are linked to the Kaniadakis \kappa-calculus. In the article, a final discussion will be devoted to the link of the q-integers to the Mersenne numbers. Besides the discussion of the previously mentioned numbers, the general aim of the paper is that of popularizing the existence of the q-calculus.

Keywords: q-calculus, q-integers, Tsallis q-entropy, Mersenne numbers

Suggested Citation

Sparavigna, Amelia Carolina, The q-Integers and the Mersenne Numbers (May 23, 2018). Available at SSRN: https://ssrn.com/abstract=3183800 or http://dx.doi.org/10.2139/ssrn.3183800

Amelia Carolina Sparavigna (Contact Author)

Polytechnic University of Turin - Department of Applied Science and Technology ( email )

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
73
Abstract Views
537
Rank
580,727
PlumX Metrics