The principal branch of an analytic multivalued function, also called a principal sheet, is a single-valued "slice"
(i.e., branch) of the function chosen that is for convenience
in referring to a specific canonical value (a so-called principal
value) of the function for each complex .

For example, the principal branch of the natural logarithm, sometimes denoted , is the one for which , and hence is equal to the value for all (Knopp 1996, p. 111). The value of a function on
its principal branch is known as its principal value.
All values of
then consist of

with ,
..., with the principal branch corresponding to . Since has only a single branch point,
all branches can be plotted to give the entire Riemann
surface.