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We analyze the conditions on the Taylor coefficients of an analytic functionto admit global analytic continuation, complementing a recent paper of Breuerand Simon on general conditions for natural boundaries to form. A new summationmethod is introduced to convert a relatively wide family of infinite sums andlocal expansions into integrals. The integral representations yield globalinformation such as analytic continuability, position of singularities,asymptotics for large values of the variable and asymptotic location of zeros.

From Taylor series of analytic functions to their global analysis