Year: 2025
Type: article
Abstract: In a previous paper, we generalized the well-known Euler-Mascheroni constant c0, in both positive and negative senses. In this sense, for each (0,1), starting from two generalizations of the string cn which converges to c0, we obtained two sequences cn, and cn,-, which converge to c and cn,-, respectively. We called these limits, c - the positive generalized Euler-Mascheroni constant or the positive generalized Euler constant, respectively c- - the negative generalized Euler-Mascheroni constant or the negative generalized Euler constant. By calculating the limits of some sequences in two different ways, we obtained the integral form of these two constants c and c- and, then, we calculated these two constants for different rational values of the number . In this paper we will present other ways of determining these generalized constants, mentioned above, and we have extended the determination of these generalized constants to different values of 1 (integers or rational numbers). With all the values obtained for c, we have presented immediate applications to determining the limits of sequences of real numbers. At the end of this paper, I proposed, to the attentive reader interested in these issues, the solution of an interesting exercise. Of course, this paper is exclusively about Mathematics Didactics and can be used / recommended to all those interested in these issues: pupils, students or Mathematics teachers.
Source: Educatia 21
Author: Teodor Dumitru Valcan
Institution: Babeș-Bolyai University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4417414137
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