The object of this paper is to investigate certain series and differential equations, generalizations of the series of Bessel and Legendre.
Throughout the paper
reducing, when p = 1, to n.
The series discussed are the following:—
a generalized form of Pn(x),
the relation between coefficients of x in successive terms being
* A short paper containing some of the results in this paper was read at the November meeting of the Society ; the paper, in its present form, is dated January 1903.