A Recursive Scheme for Improving the Original Rate of Convergence to the Euler—Mascheroni Constant

We have used Euler-Maclaurin summation to develop a recursive scheme for modifying the original approximation for the Euler-Mascheroni constant γ. Convergence to γ resulting from successively employing the proposed scheme has been significantly accelerated while the form of the approximation originally introduced by Euler is still preserved.