An entire function is a complex function that is holomorphic (complex differentiable) at every point in the complex plane. This characteristic means that these functions are defined and differentiable everywhere, allowing them to exhibit unique properties, especially in relation to their growth and behavior at infinity. Key concepts related to entire functions include their applications to the maximum modulus principle, behavior characterized by Liouville's theorem, and representation through the Weierstrass factorization theorem.
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