  The spheroidal wave functions are investigated in the case m=1. The integral
equation is obtained for them. For the two kinds of eigenvalues in the
differential and corresponding integral equations, the relation between them
are given explicitly. Though there are already some integral equations for the
spheroidal equations, the relation between their two kinds of eigenvalues is
not known till now. This is the great advantage of our integral equation, which
will provide useful information through the study of the integral equation.
Also an example is given for the special case, which shows another way to study
the eigenvalue problem.
