In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, a principal branch is a function which selects one
branch
A branch, sometimes called a ramus in botany, is a woody structural member connected to the central trunk of a tree (or sometimes a shrub). Large branches are known as boughs and small branches are known as twigs. The term '' twig'' usuall ...
("slice") of a
multi-valued function. Most often, this applies to functions defined on the
complex plane.
Examples
Trigonometric inverses
Principal branches are used in the definition of many
inverse trigonometric functions, such as the selection either to define that
: