Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

90 PROF. FORSYTH, ON THE INTEGRALS OF SYSTEMS OF EQUATIONS.
from vanishing for integer values of X, /a, v such that X + / + v 2. The real parts of
l>, 2 are supposed to be positive.
The instances that can occur are obviously for X = O in the first set and j =0 in
the second set; both are included in the form
e = im + ^,
where e and q are the roots of the quadratic, and + v > 2. The cases J = O, = 1,
have already been discussed. For the remaining cases, we have the theorem: The
double infinitude of non-regular integrals vanishing with t are then regular functions of
t, t1, t'+v" log t, where, and v are integers. It can be established in the same manner as
the similar theorems in the preceding sections.