Abstract
ABSTRACT A modification of Watson's lemma for Laplace transforms was introduced in [Nielsen, 1906], deriving a new asymptotic expansion for large with the extra property of being convergent as well. Inspired in that idea, in this paper we derive asymptotic expansions of two-dimensional Laplace transforms for large and that are also convergent. The expansions of are accompanied by error bounds. Asymptotic and convergent expansions of some special functions are given as illustration.
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