NEW REPRESENTATIONS FOR THE EULER-MASCHERONI CONSTANT AND INEQUALITIES FOR THE GENERALIZED-EULER-CONSTANT FUNCTION
(i) We establish new representations for the Euler-Mascheroni constant gamma in terms of the gamma and psi functions. (ii) A class of two-sided inequalities for the generalized-Euler-constant function are presented. These inequalities provide the lower and upper bounds on the error of approximating the generalized-Euler-constant function by means of a power series.
euler-mascheroni constant inequality generalized-euler-constant function gamma function psi (or digamma) function