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In theoretical physics, resurgence is used to treat infinities in quantum field theory.



Resurgent functions are divergent power series whose Borel transforms converge in a neighborhood of the origin and give rise, by means of analytic continuation, to (usually) multi-valued functions. These functions have merely isolated singularities without singularities that form cuts with dimension one or greater.


Example 1



The French mathematician Jean Écalle developed a theory of resurgent functions in 1984.