Abel summation is a mathematical technique used to assign values to certain infinite series that may not converge in the traditional sense. It involves transforming a series into a related function, often a power series, and then evaluating the limit of that function as it approaches a specific point. This method can help in analyzing the behavior of series and understanding their convergence properties. The process typically involves two main steps: first, defining a function based on the series, and second, taking the limit of that function as a variable approaches a particular value. Abel summation is particularly useful in number theory and analysis, providing insights into series that are otherwise difficult to evaluate.