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spheroidal wave functions are investigated in the case $m = 1$. The integral equation is obtained for them. There are two
kinds of eigenvalues in the differential and corresponding integral equations, and
the relation between them is given explicitly. 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.