Abstract

In the paper under discussion, Dr. Negi has investigated the boundaries of convergence of three power series and has considered the behavior of the series on their respective boundaries of convergence. For convenience he reduces the series to their standard forms. By consulting Bromwich (1964), he finds the boundaries of convergence and with the help of a theorem (Morse and Feshbach, 1953), derives three relations, one for each series, for testing the presence of singularities on the boundaries of convergence. Dr. Negi (1968) states that the relations predict all the three series would always be divergent on their respective boundaries of convergence. In what follows it is shown that

  • (1) the relations found by Dr. Negi tell us that the singular points are ordinary and many ordinary points on the boundaries are singular,

  • (2) the relations do not predict the behavior of the series, and

  • (3) the last two series do not diverge on their respective boundaries of convergence.

First Page Preview

First page PDF preview
You do not currently have access to this article.