Borel resummation of an integral

  1. let be the integral [tex] \int_{0}^{\infty}dxf(x)e^{ix} [/tex]

    from the technique of Borel resummation applied to series , would it be corect to assign the 'Borel resummation' for the integral above as

    [tex] \int_{0}^{\infty}\int_{0}^{\infty}dtdx \frac{t^{x}f(x)e^{ix-t}}{\Gamma (x+1)} [/tex]
     
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