The Method of Difference Equations Applied to the Summation of Certain Series Involving Legendre and Bessel Functions

In this paper, certain series, finite as well as infinite, involving Legendre and Bessel functions as well as their allied functions, are summed up by the help of the linear difference equations satisfied by these functions. Some of the results are not new, having been deduced by other writers by special methods. But the methods of this paper are claimed to be quite elegant and elementary, and are capable of being applied to the summation of several series whose terms satisfy certain linear difference equations of the second order. The methods can also possibly be extended so as to be applicable to some other types of linear difference equations.