# §15.4 Special Cases

## §15.4(i) Elementary Functions

The following results hold for principal branches when , and by analytic continuation elsewhere. Exceptions are (15.4.8) and (15.4.10), that hold for , and (15.4.12), (15.4.14), and (15.4.16), that hold for .

compare §15.2(ii).

For an extensive list of elementary representations see Prudnikov et al. (1990, pp. 468–488).

## §15.4(ii) Argument Unity

### ¶ Dougall’s Bilateral Sum

This is a generalization of (15.4.20). If are not integers and , then