Definition:Algebraic Function/Complex

Definition

Let $w$ be a solution to the polynomial equation:

$\map {p_0} z + \map {p_1} z w + \dotsb + \map {p_{n - 1} } z w^{n - 1} + \map {p_n} z w^n = 0$

where $\map {p_0} z \ne 0, \map {p_1} z, \dotsc, \map {p_n} z$ are complex polynomial functions in $z$.

Then $w = \map f z$ is a (complex) algebraic function:

Also see

• Definition:Real Algebraic Function

• Results about algebraic functions can be found here.

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $10$