Hadamard Factorisation Theorem
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Theorem
Let $f: \C \to \C$ be an entire function of order $1$.
Let $\rho_1,\rho_2,\ldots$ be an increasing enumeration of the zeros of $f$, counted with multiplicity.
Then there exist constants $a(f)$, $b(f)$ such that
- $\displaystyle f(z) = \exp(a+bz) \prod_{k=1}^\infty \left( 1 - \frac z{\rho_k} \right) \exp\left( \frac z{\rho_k} \right)$
Proof
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Source of Name
This entry was named for Jacques Salomon Hadamard.
