On Some Series Dependent on a Parameter Which Generalize Euler’s Constant

Paul Bracken

Abstract

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.

Keywords

Euler’s constant, sequence, series, convergence, asymptotic

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