We want to study the asymptotic behavior of the complete elliptic integral of the first kind when . This is motivated, for example, by the occurrence of as capacitance of a circular capacitor with slit (or similar geometries--see for example [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 behavior 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.

south.rotol.ramk.fi/~keranen/IMS99/paper21/ims99paper21.nb