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Is there any way to express $$\sum_{k=1}^\infty \frac{1}{k^k}.$$ without a sum? I know this converges to ≈ 1,2913 by calculating it, by how can you express this another way? Also, is this number transcendental?

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  • $\begingroup$ Very related to "Closed" form for $\sum \frac{1}{n^n}$. $\endgroup$ Commented Jul 29, 2013 at 13:52
  • $\begingroup$ Are you interested in this problem from pure curiosity, or do you have a specific reason for wanting to know? $\endgroup$
    – Kenta S
    Commented Nov 18, 2017 at 9:11

2 Answers 2

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Here's another way: Sophomore's dream.

(From a computational point of view, this may be no more useful than the sum.)

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Consider the integral

$$ \int_{0}^{1} x^{-x} dx . $$

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