Abstract
Asymptotic formulae for the eulerian numbers
A(n, k)
for
n
≫ 1 are obtained directly from their recursion relation by the ray method and the method of matched asymptotic expansions. These are formal methods, so they do not prove that the formulae are asymptotic, although they suggest it. The formulae agree with the previously known results where those results are valid. They also agree very well with the exact values of
A(n, k)
for 1 ≼
n
≼ 170, and the agreement improves as
n
increases.
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