Euler's number | |
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e 2.71828...[1] | |
General information | |
Type | Transcendental |
History | |
Discovered | 1685 |
By | Jacob Bernoulli |
First mention | Quæstiones nonnullæ de usuris, cum solutione problematis de sorte alearum, propositi in Ephem. Gall. A. 1685 |
Named after |
Part of a series of articles on the |
mathematical constant e |
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Properties |
Applications |
Defining e |
People |
Related topics |
The number e is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of the natural logarithm function. It is the limit of as n tends to infinity, an expression that arises in the computation of compound interest. It is the value at 1 of the (natural) exponential function, commonly denoted It is also the sum of the infinite series There are various other characterizations; see § Definitions and § Representations.
The number e is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted . Alternatively, e can be called Napier's constant after John Napier.[2][3] The Swiss mathematician Jacob Bernoulli discovered the constant while studying compound interest.[4][5]
The number e is of great importance in mathematics,[6] alongside 0, 1, π, and i. All five appear in one formulation of Euler's identity and play important and recurring roles across mathematics.[7][8] 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.[3] To 30 decimal places, the value of e is:[1]
Miller
was invoked but never defined (see the help page).