The asymptotic expansion of a convolution integral (Q1195415)

The asymptotic behaviour of the convolution integral \(J(s)=\int_ 0^ s(\nu+x)^{-\alpha}(2+\mu-x)^{-\beta}dx\), \(\mu,\nu>0\), \(\alpha,\beta<1\), as \(s\to\infty\) is investigated. The first term of the expansion leads to \(J(s)\sim B(1-\alpha,1-\beta)s^{1-\alpha-\beta}\).