# §10.18 Modulus and Phase Functions

## §10.18(i) Definitions

For and

where , , , and are continuous real functions of and , with the branches of and fixed by

10.18.3
,.

10.18.13
10.18.15.
10.18.16

## §10.18(iii) Asymptotic Expansions for Large Argument

As , with fixed and ,

The remainder after terms in (10.18.17) does not exceed the th term in absolute value and is of the same sign, provided that .