Errata: The Cauchy principal value and the Hadamard finite part integral as values of absolutely convergent integrals (E.A. Galapon, J. Math. Phys. 57, 033502 (2016))
Equations 30 and 31 should read as follows: $\setCounter{29}$ \begin{eqnarray} \int_a^{x_0-\epsilon} \frac{f(x)}{(x-x_0)^{n+1}}\mbox{d}x &=& -\sum_{k=0}^{n-1} \frac{f^{(k)}(x_0)}{k!(n-k)} \left(\frac{1}{(-\epsilon)^{n-k}} – \frac{1}{(a-x_0)^{n-k}}\right) \nonumber \\ && + \frac{f^{(n)}(x_0)}{n!} \left(\ln \epsilon – \ln(x_0-a)\right)\nonumber \\ && + \sum_{k=n+1}^{\infty} \frac{f^{(k)}(x_0)}{k!(k-n)} \left((-\epsilon)^{k-n}-(a-x_0)^{k-n}\right) \end{eqnarray}\begin{eqnarray} \int_{x_0+\epsilon}^b \frac{f(x)}{(x-x_0)^{n+1}}\mbox{d}x &=& -\sum_{k=0}^{n-1} \frac{f^{(k)}(x_0)}{k!(n-k)} \left(\frac{1}{(b-x_0)^{n-k}} – \frac{1}{\epsilon^{n-k}}\right) \nonumber \\ && + \frac{f^{(n)}(x_0)}{n!} \left(\ln (b-x_0) – \ln\epsilon\right)\nonumber \\ && + \sum_{k=n+1}^{\infty}… Read More »