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.

Power series (including lacunary series) (msc 30B10), Integration, integrals of Cauchy type, integral representations of analytic functions (msc 30E20), Convergence and divergence of series and sequences of functions (msc 40A30)
Modelling, Analysis and Simulation [MAS]
Computational Dynamics

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