Numerical evaluation of the high accuracy of an integral with power singularities (Q1282469)

This paper is devoted to the development of a numerical approach for the following integral \[ A(\alpha,x)= \int^1_0t^{\alpha-1} (1-t)^{-\alpha} (1-xt)^{\alpha-1}dt, \quad 0<\alpha<1,\;0\leq x<1 \] near \(x=1\) where it diverges. An algorithm for the numerical evaluation of the integral \(A(\alpha,x)\) and an error estimate are presented, along with a numerical example.