ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D169
Napier's constant
Formulation 0
Let $!$ be the D6: Natural number factorial function.
The Napier's constant is the D993: Real number \begin{equation} e : = \lim_{N \to \infty} \sum_{n = 0}^N \frac{1}{n!} \end{equation}
Formulation 1
Let $!$ be the D6: Natural number factorial function.
The Napier's constant is the D993: Real number \begin{equation} e : = \sum_{n = 0}^{\infty} \frac{1}{n!} \end{equation}
Formulation 2
Let $!$ be the D6: Natural number factorial function.
The Napier's constant is the D993: Real number \begin{equation} e : = \frac{1}{0!} + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \cdots \end{equation}
Formulation 3
Let $!$ be the D6: Natural number factorial function.
The Napier's constant is the D993: Real number \begin{equation} e : = \frac{1}{1} + \frac{1}{1} + \frac{1}{1 \cdot 2} + \frac{1}{1 \cdot 2 \cdot 3} + \frac{1}{1 \cdot 2 \cdot 3 \cdot 4} + \cdots \end{equation}