A New Effective Asymptotic Formula for the Stieltjes Constants

We derive a new integral formula for the Stieltjes constants. The new formula permits easy computations as well as an exact approximate asymptotic formula. Both the sign oscillations and the leading order of growth are provided. The formula can also be easily extended to generalized Euler constants

On the Power Series Expansion of the Reciprocal Gamma Function

Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values of the indices. Both the sign oscillations and the leading order of growth are given.Comment: Corrected a sign in equation (3.21) due to a minor error in (3.19) where the fraction was inadvertently inverted. Now the rough approximation provides an elementary proof that the order of the reciprocal gamma function is 1 and that its type is maxima