In this paper we propose to study the behavior of series of complex numbers, or of vectors in two dimensions; and to generalize this study to the case of vectors in n dimensions. The particular properties to be studied are ...

In the classic memoirs of Sturm and Liouville, two classes of theorems are found concerning sets of orthogonal functions. The first deal with the number of sign-changes in [phi]3, and the second with the number of sign-changes ...

In this present paper we will develop some theorems concerning the degree of convergence of certain series, in particular a Fourier's series, a Legendre's series, and a series of Bessel's functions. Before proceeding ...

The author suggests methods for determining errors in graphical computations and discusses errors in the graphical methods in the infinitesimal calculus.