Hadamard finite part

Summary

The Hadamard finite part gives a value to an integral that diverges because the integrand has a non-integrable singularity, such as $\int_{-1}^{1} \frac{\varphi(t)}{t^2}\, dt$. One cuts out a small neighbourhood of the singularity, computes the integral, and drops the terms that blow up as the neighbourhood shrinks. It extends the Cauchy principal value, which handles poles of first order. Finite part integrals are the integrals in hypersingular integral equations.