Two-point Taylor Expansions of Analytic Functions
نویسندگان
چکیده
In deriving uniform asymptotic expansions of a certain class of integrals one encounters the problem of expanding a function, that is analytic in some domain Ω of the complex plane, in two points. The first mention of the use of such expansions in asymptotics is given in [1], where Airy-type expansions are derived for integrals having two nearby (or coalescing) saddle points. This reference does not give further details about two-point Taylor expansions, because the coefficients in the Airy-type asymptotic expansion are derived in a different way. To demonstrate the application in asymptotics we consider the integral
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