On convergent and divergent imaginary series. Summation of some convergent imaginary series. Notations used to represent imaginary functions that we find by evaluating the sum of such series.

Be the sum of the first n terms of this series. Depending on whether or not s _n converges towards a fixed limit∈dex{limit} for increasing values of n, we say that series (3) is convergent and that it has this limit as its sum, or else that it is divergent and it does not have a sum. The first case evidently occurs if the two sums.