# §28.26 Asymptotic Approximations for Large

## §28.26(i) Goldstein’s Expansions

Denote

where

28.26.3

Then as with fixed in and fixed ,

28.26.4
28.26.5

The asymptotic expansions of and in the same circumstances are also given by the right-hand sides of (28.26.4) and (28.26.5), respectively.

For additional terms see Goldstein (1927).

## §28.26(ii) Uniform Approximations

See §28.8(iv). For asymptotic approximations for see also Naylor (1984, 1987, 1989).