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The case given by the fundamental theorem of algebra is incorporated here. If the sequence <math>\{a_n\}</math> is finite then we can take <math>p_n = 0</math>, <math>m=0</math> and <math>e^{g(z)}=c</math> to obtain <math>\, f(z) = c\,{\displaystyle\prod}_n (z-a_n)</math>.
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The trigonometric functions [[sine]] and [[cosine]] have the factorizations
<math display=block>\sin \pi z = \pi z \prod_{n\neq 0} \left(1-\frac{z}{n}\right)e^{z/n} = \pi z\prod_{n=1}^\infty \left(1-\left(\frac{z}{n}\right)^2\right)</math>
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