Saverio Salerno

**Abstract**

We want to study the asymptotic behaviour of the complete elliptic
integral of the first kind K(m) when m->1. This is motivated, for
example, by the occurrence of K(m) as capacitance of a circular
capacitor with slit (or similar geometries - see e.g. [9]) -, m being essentially
the ratio between the slit's length and the radius of the circle. We show
that the analysis of the asymptotic behaviour can be done in several ways
(including series expansion and summation, symbolic integration and computation
of limits) using both the numerical and symbolical capabilities of state-of-the-art
Computer Algebra Systems.