Branch point

Point of interest for complex multi-valued functions

In the mathematical field of complex analysis, a branch point of a multivalued function is a point such that if the function is n {\displaystyle n} -valued (has n {\displaystyle n} values) at that point, all of its neighborhoods contain a point that has more than n {\displaystyle n} values. Multi-valued functions are rigorously studied using Riemann surfaces, and the formal definition of branch points employs this concept. Branch points fall into three broad categories: algebraic branch points, transcendental branch points, and logarithmic branch points.

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