Abel's theorem

The Abelian limit theorem is a mathematical theorem from sub-area of analysis. He describes the conditions under which a defined as a power series function can continue steadily on the edges of the convergence interval and reads as follows:

Application

The inverse of the tangent function on the interval possesses the following representation as a power series:

The series converges by the Leibniz criterion. Since, the Abelian limit theorem gives the identity