Euler's constant, generalized (II) - other ways of determining

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.

Authors

Publication Details

Journal
Educatia 21
Published
2025-11-28
DOI
https://doi.org/10.24193/ed21.2025.31.29
Primary Topic
Advanced Mathematical Theories
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Euler's constant, generalized (II) - other ways of determining

Teodor Dumitru Vălcan
Educatia 21
Advanced Mathematical Theories
article

Euler's constant, generalized (II) - other ways of determining

Teodor Dumitru Vălcan
article en

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.

Educatia 21(31)
Openalex Percentile: Top 55%
Advanced Mathematical Theories
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.