  We analyze the conditions on the Taylor coefficients of an analytic function
to admit global analytic continuation, complementing a recent paper of Breuer
and Simon on general conditions for natural boundaries to form. 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.
