# Borel resummation of an integral

by zetafunction
Tags: borel, integral, resummation
 P: 399 let be the integral $$\int_{0}^{\infty}dxf(x)e^{ix}$$ from the technique of Borel resummation applied to series , would it be corect to assign the 'Borel resummation' for the integral above as $$\int_{0}^{\infty}\int_{0}^{\infty}dtdx \frac{t^{x}f(x)e^{ix-t}}{\Gamma (x+1)}$$