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The multiplication theorem over a field of [[characteristic zero]] does not close after a finite number of terms, but requires an [[infinite series]] to be expressed. Examples include that for the [[Bessel function]] <math>J_\nu(z)</math>:
:<math>
\lambda^{-\nu} J_\nu (\lambda z) = \sum_{n=0}^\infty \frac{1}{n!}
\left(\frac{(1-\lambda^2)z}{2}\right)^n
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