U+212F Script Small E

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The number e is a mathematical constant, approximately equal to 2.71828, that is the base of the natural logarithm.

The number e is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler's constant, a different constant typically denoted $\gamma$. Alternatively, e can be called Napier's constant after John Napier. The constant was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest.

The number e is of great importance in mathematics, alongside 0, 1, π, and i. All five appear in one formulation of Euler's identity $e^{i\pi }+1=0$ and play important and recurring roles across mathematics. Like the constant π, e is irrational, meaning that it cannot be represented as a ratio of integers, and moreover it is transcendental, meaning that it is not a root of any non-zero polynomial with rational coefficients. To 40 decimal places, the value of e is: