A singular integral is an integral whose integrand reaches an infinite value at one or more points in the domain of integration. Even
so, such integrals can converge, in which case, they are said to exist. (If they
do not converge, they are said not to exist.) The most commonly encountered example
of a singular integral is the Hilbert transform.
(However, note that the logarithmic integral
is not singular, since it converges in the classical Riemann sense.)
In general, singular integrals can be defined by eliminating a small space including the singularity, and then taking the limit as this small space disappears.
