Borel resummation of an integral

by zetafunction
Tags: borel, integral, resummation
zetafunction is offline
Jan7-11, 03:48 AM
P: 399
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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