Taylor expansions of analytic functions are considered with respect to two points.Cauchy-type formulas are given for coefficients and remainders inthe expansions, and the regions of convergence are indicated.It is explained how these expansions can be used in deriving uniformasymptotic expansions of integrals. The method is also used for obtaining Laurentexpansions in two points.

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Modelling, Analysis and Simulation [MAS]
Computational Dynamics

López, J. L., & Temme, N. (2002). Two-point Taylor expansions of analytic functions. Modelling, Analysis and Simulation [MAS]. CWI.