Definition:Exponent of Convergence
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Definition
Let $\sequence {a_n}$ be a sequence of nonzero complex numbers.
The exponent of convergence of $\sequence {a_n}$ is the infimum of $\tau \ge 0$ for which the series $\ds \sum_{n \mathop = 1}^\infty \size {a_n}^{-\tau}$ converges.
The exponent of convergence of a finite sequence is $0$.
Also see
- Definition:Rank of Entire Function
- Exponent of Convergence is Less Than Order, where it is shown that a function of finite order has finite exponent of convergence