# §11.2 Definitions

## §11.2(i) Power-Series Expansions

Principal values correspond to principal values of ; compare §4.2(i).

The expansions (11.2.1) and (11.2.2) are absolutely convergent for all finite values of . The functions and are entire functions of and .

11.2.3

Principal values of and correspond to principal values of the functions on the right-hand sides of (11.2.5) and (11.2.6).

Unless indicated otherwise, , , , and assume their principal values throughout the DLMF.

## §11.2(iii) Numerically Satisfactory Solutions

In this subsection and are arbitrary constants.

When , , and , numerically satisfactory general solutions of (11.2.7) are given by

(11.2.11) applies when is bounded, and (11.2.12) applies when is bounded away from the origin.

When , numerically satisfactory general solutions of (11.2.9) are given by

(11.2.16) applies when with bounded. (11.2.17) applies when with bounded away from the origin.