# §10.67 Asymptotic Expansions for Large Argument

## §10.67(i) , and Derivatives

Define and as in §§10.17(i) and 10.17(ii). Then as with fixed,

The contributions of the terms in , , , and on the right-hand sides of (10.67.3), (10.67.4), (10.67.7), and (10.67.8) are exponentially small compared with the other terms, and hence can be neglected in the sense of Poincaré asymptotic expansions (§2.1(iii)). However, their inclusion improves numerical accuracy.

As