  This paper presents a family of rapidly convergent summation formulas for
various finite sums of analytic functions. These summation formulas are
obtained by applying a series acceleration transformation involving Stirling
numbers of the first kind to the asymptotic, but divergent, expressions for the
corresponding sums coming from the Euler-Maclaurin summation formula. While it
is well-known that the expressions obtained from the Euler-Maclaurin summation
formula diverge, our summation formulas are all very rapidly convergent and
thus computationally efficient.
