Proceedings of the Edinburgh Mathematical Society

Table of Contents - Volume 21 - 1902  

Research Article

Generalized forms of the Series of Bessel and Legendre*

Rev. F. H. Jackson

The object of this paper is to investigate certain series and differential equations, generalizations of the series of Bessel and Legendre.

Throughout the paper

S0013091500034519_eqnU1

reducing, when p = 1, to n.

The series discussed are the following:—

S0013091500034519_eqn1

a generalized form of Pn(x),

the relation between coefficients of x in successive terms being

S0013091500034519_eqn2

Footnotes

* 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.