Error Analysis of a Computation of Euler's Constant*

A complete error analysis of a computation of y, Euler's constant, is given. The results have been used to compute -y to 7114 places and this value has been deposited in the UMT file. 1. Introduction. In a paper on ergodic computations with continued fractions (1), we used 3561 decimal places of y, Euler's constant, as given by Sweeney (7) to compute 3420 partial quotients of the continued fraction expansion of T. The partial quotients were sent to the Unpublished Manuscript Tables file and were there com- pared by Dr. Wrench with those given by Choong et al. (3). Some disagreements were found and it was eventually decided to recompute Sweeney's value. This involved a careful reading of Sweeney's method and, as his error analysis is not detailed, a distinct error analysis resulted. This analysis is presented here.