An asymptotic expansion for the semi‐infinite sum of Dirac‐ δδ functions

摘要

xml:id="mma4479-para-0001"> In this paper, we derive an asymptotic expansion for the semi‐infinite sum of Dirac‐ δ functions centered at discrete equidistant points defined by the set N a = { x ∈ R : ? n ∈ N ∧ x = n a , ? a 0 } . The method relies on the Laplace transform of the semi‐infinite sum of Dirac‐ δ functions. The derived series distribution takes the form of the Euler‐Maclaurin summation when the distributions are defined for complex or real‐valued continuous functions over the interval 展开▼