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Is there a function $f(x)$ such that $f(f(x))=e^x$?

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#exponential-function #functional-equations
338
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How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?

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#calculus #limits #exponential-function
125
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Surjectivity of the complex exponential without using $π$

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#complex-analysis #exponential-function
102
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$k'=k$ only for $e^x$

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#derivatives #exponential-function
644
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Solving $2^{2x+1} - 2^{x+4} = 2^3 - 2^x$

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#exponential-function #quadratics
3.4k
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Proof that at most one of $e\pi$ and $e+\pi$ can be rational

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#proof-verification #exponential-function #pi #transcendental-numbers #rationality-testing
1.6k
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Proof that $e^x$ can be expressed in a series of ascending powers of $x$

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#power-series #exponential-function
197
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How to continue solving? Perfect Cuboid

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#modular-arithmetic #logarithms #exponential-function #pythagorean-triples
44
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Basic Variable Isolation

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#exponential-function
364
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Transformation Ricker equation

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#logarithms #exponential-function
86
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Rewrite formula using exponential generating functions

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#recurrence-relations #exponential-function #generating-functions
68
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Prove convergence of $(1-\frac xk)^k$ as $k\to\infty$ using arithmetic-geometric mean

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#calculus #limits #convergence-divergence #exponential-function #means
1.1k
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Calculating $ \lim_{n\to \infty} (1+\sin({1}/{n}))^{n}$ without L'Hopital or series expansions

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#calculus #limits #exponential-function #infinity
157
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what to do with: logarithmic, trigonometric and exponential inequalities with variable outside

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#calculus #real-analysis #algebra-precalculus #inequality #exponential-function
9.4k
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Adding complex exponentials

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#complex-analysis #complex-numbers #exponential-function

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