The principal value of an analytic multivalued function is the single value chosen by convention to be returned for a given argument. Complex multivalued functions have multiple branches in the complex plane, with those corresponding to the principal values known as the principal branch. For example, the principal branch of the natural logarithm, sometimes denoted Ln z, is the one for which ln1 = 0, and hence is equal to the value ln x for all x>0. All values of ln z then consist of ln z = 2π i k + Ln z,

Cauchy principal value | principal branch | principal square root