Open AccessOn Some Series Dependent on a Parameter Which Generalize Euler’s Constant
Author(s) -
Paul Bracken
Publication year - 2019
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v12i1.3346
Subject(s) - mathematics , constant (computer programming) , series (stratigraphy) , euler's formula , euler summation , convergence (economics) , mathematical analysis , euler equations , semi implicit euler method , backward euler method , paleontology , computer science , economics , biology , programming language , economic growth
Series which depend on a parameter and generalize the constant discovered by Euler are introduced and studied. Convergence results are established. An infinite series expansion is obtained from these generalized formulas which can be used to evaluate the generalized constant. Euler’s constant can be obtained as a special case. Some asymptotic results are formulated and limits of some closely related sequences are given at the end.