Note on the Poincaré boundary-value problem
E. E. Jones · Quarterly of Applied Mathematics · 1961
which may be solved by quadrature, Is = a f u~2F(u) du = Kf/2)1/2{cos a2 -sin a2 -2a[C(a) + /S(a)]}. J aFinally, the most significant integral from the point of view of the physical problem J, = f {[C(x + a) -C{x -a)]2 + [S(® + a) -S(x -a)]2} dx Jo -I3 + li ~ 2/5 = TTd, a remarkably simple result.