A branch point whose neighborhood of values wrap around the range a finite number of times as their complex arguments varies from 0 to a multiple of is called an algebraic branch point of order . Such points correspond to the point under functions of the form .

Formally, an algebraic branch point is a singular boundary point of one sheet of a multivalued function about which a finite number of distinct sheets hang together like the surface for at the origin and for which the domain of values affixed to these sheets in a neighborhood of , which can be developed in a series of the form

is such that only a finite number (or zero) negative power of appear in the expansion (Knopp 1996, Part II, p. 143).