Abstract
Mellin transforms are used here to find asymptotic approximations for functions defined by series. The simplest cases are those of the form Σ n=1 ∞ u(nx). Such series are called separable here, because the given function u is sampled at points whose variation with n and x is separated. Nonseparable series are analysed by first approximating them by separable series. Both types of series arise in the theory of electromagnetic waveguides and in the theory of linear water waves; several examples are worked out in detail
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