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.