On some consequences of the Laplacian's singularity at the origin in spherical coordinates

In this article we address the singular behavior of the Laplace operator in spherical coordinates, which has been established in our earlier works. This singularity has many non-trivial consequences. In this article we consider only the simplest ones, which are connected to the solution of the Laplace equation in various classical books and lectures. We show how solutions, which have a fictitious singular behavior at the origin can be avoided. This material may be useful in physics education both for students and teachers as well. (paper)