  A new summation method is introduced to convert a relatively wide family of
infinite sums and local expansions into integrals. The integral representations
yield global information such as analytic continuability, position of
singularities, asymptotics for large values of the variable and asymptotic
location of zeros. There is a duality between the global analytic structure of
the reconstructed function and the properties of the coefficients as a function
of their index. Borel summability of a class of divergent series follow as a
byproduct.
