Contour Integral Representations of Finite-part Integrals with Logarithmic Singularities

Reynaldo P. Ylanan, Eric A. Galapon

The integral ${\int }_0^{a}f(t)t^{-s}\mathrm{d}t$ diverges for $\text{Re}(s)\ge \hat{I}»+1$, where $\hat{I}»$ is the order of the first non-vanishing derivative of $f(t)$ at the origin. With…