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
![sum_(n=-infty)^inftyc_n[(z-z_0)^(1/p)]^n,](/images/equations/AlgebraicBranchPoint/NumberedEquation1.svg) |
is such that only a finite number (or zero) negative power of 
appear in the expansion (Knopp 1996, Part II,
p. 143).
