 TOPICS  # Algebraic Branch Point

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).

Branch Point, Logarithmic Branch Point

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## References

Knopp, K. Theory of Functions Parts I and II, Two Volumes Bound as One, Part I. New York: Dover, Part II, pp. 142-143, 1996.

## Referenced on Wolfram|Alpha

Algebraic Branch Point

## Cite this as:

Weisstein, Eric W. "Algebraic Branch Point." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlgebraicBranchPoint.html