search for: meromorph

...n of numeric values in real & imaginary parts), the usual mathematical answer for atan(1i) may no longer be relevant. The tangent function has an essential singularity at complex infinity (the compactification point in the Riemann sphere, which I consider the natural extension for the study of meromorphic functions, for example making the tangent function well defined on the whole plane), so the usual extension of the plane does not give us an answer for atan(1i). However, another possible extension is the Cartesian square of the extended real line, and in that extension continuity suggests that t...