Abstract
Recently, there has been a surge of practical and theoretical interest on the part of mathematical physicists, classical analysts and abstract analysts in the subject of exponential asymptotics, or hyperasymptotics, by which is meant asymptotic approximations in which the error terms are relatively exponentially small. Such approximations generally yield much greater accuracy than classical asymptotic expansions of Poincaré type, for which the error terms are algebraically small: in other words, they lead to “exponential improvement.” They also enjoy greater regions of validity and yield a deeper understanding of other aspects of asymptotic analysis, including the Stokes phenomenon.
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Daalhuis, A.B.O. (2003). Exponential Asymptotics. In: Koelink, E., Van Assche, W. (eds) Orthogonal Polynomials and Special Functions. Lecture Notes in Mathematics, vol 1817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44945-0_6
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DOI: https://doi.org/10.1007/3-540-44945-0_6
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