# Questions tagged [exponential-function]

For question involving exponential functions and questions on exponential growth or decay.

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### A method to evaluate functional roots of $e^x$

I've an idea to find exact function $f(x)$ such that $f(f(x))=e^x$. But it involves solving complicated systems of non-linear equations, the skills for which I don't have. Here's how I intend to do ...
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### Expansion of Gaussian function in a series of exponential functions

Trying to solve a complicated integral, I got interested as a side question in the following problem. Suppose that $f(x)=\exp(-x^2/2)$ is a standard Gaussian function. Is it ever possible to represent ...
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### Showing the exponential and logarithmic functions are unique in satisfying their properties

The question asks to prove that there exists a unique function defined on $\Bbb R$ and satisfying the following conditions: 1) $f(1) = a$ $(a>0, a \neq 0)$ 2) $f(x_1) \cdot f(x_2) = f(x_1 + x_2)$...
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