This thesis is divided into two parts. In
the first part, I have studied the properties of
certain functions of the confluent hypergeometric
types, viz. Functions of Mathieu, Whittaker,
Weber and Bateman. The development of Heaviside's
operational method and the perfection of the symbolic calculus by the researches of Carson, Van
der Pol and
and others have made it possible to study the
functions more easily. The large number* of
papers that have recently been published, shows
at once its recognition as a powerful instrument
in mathematical investigations by the mathematicians. In this thesis I have taken help of the
method of this calculus to study the functions.
The second part which I have denoted as supplementary papers, deals with two distinct subjects:
(i) Automorphic Functions, and (ii) Relativity.
They are, therefore, on subjects quite different
from that of the first part.