Derivation and implementation of an algorithm for singular integrals (Q1822447)

We give the possibility to evaluate the following integral: (1) \(I=\int^{a}_{b}w(t)g(t)dt\) where the weight function w(t) is a linear combination of functions having algebraic and logarithmic singularities either in a or in b. In order to evaluate the integral (1) we suggest and synthesize an algorithm for the construction of a class of extended Gaussian quadrature rules. We also describe and comment a Fortran code which carries out this algorithm, and we provide some meaningful numerical results and comparisons.