The Weierstrass Factorization Theorem states that every entire function can be represented as a product built from its zeros together with a factor coming from an entire function that has no zeros at all, extending to entire functions with infinitely many zeros the way a polynomial factors according to its roots. Named for Karl Weierstrass, it is a foundational result of complex analysis used to construct entire functions with prescribed zeros.
Facts
StatementEvery entire function can be written as a product built from factors accounting for its zeros together with a nonvanishing entire function, extending the fundamental theorem of algebra's factorization of polynomials to entire functions. 1 Connections
Sources
1. Weierstrass Factorization Theorem (Wikipedia)
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In mathematics, and particularly in the field of complex analysis, the Weierstrass factorization theorem asserts that every entire function can be represented as a (possibly infinite) product involving its zeroes.
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