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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.
Book chapter

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.

R.E. Bradley and C.E. Sandifer
Cauchy’s Cours d’analyse, pp.181-215
Sources and Studies in the History of Mathematics and Physical Sciences, Springer
2009
DOI: https://doi.org/10.1007/978-1-4419-0549-9_9

Abstract

Numbers Integers Convergent Divergent
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.
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