Resummation

In mathematics and theoretical physics, resummation is a procedure to obtain a finite result from a divergent sum (series) of functions. Resummation involves a definition of another (convergent) function in which the individual terms defining the original function are re-scaled, and an integral transformation of this new function to obtain the original function. Borel resummation is probably the most well-known example.The simplest method is an extension of a variational approach to higher order based on a paper by R.P. Feynman and H. Kleinert.In quantum mechanics it was extended to any order here, and in quantum field theory here.See also Chapters 16–20 in the textbook cited below.