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  2. e (mathematical constant) - Wikipedia

    en.wikipedia.org/wiki/E_(mathematical_constant)

    The number e is a mathematical constant approximately equal to 2.71828 that is the base of the natural logarithm and exponential function.It 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 .

  3. Euler's constant - Wikipedia

    en.wikipedia.org/wiki/Euler's_constant

    Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma (γ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log:

  4. List of representations of e - Wikipedia

    en.wikipedia.org/wiki/List_of_representations_of_e

    The mathematical constant e can be represented in a variety of ways as a real number. Since e is an irrational number (see proof that e is irrational ), it cannot be represented as the quotient of two integers , but it can be represented as a continued fraction .

  5. Transcendental number - Wikipedia

    en.wikipedia.org/wiki/Transcendental_number

    The Euler–Mascheroni constant γ: In 2010 it has been shown that an infinite list of Euler-Lehmer constants (which includes γ/4) contains at most one algebraic number. [ 51 ] [ 52 ] In 2012 it was shown that at least one of γ and the Gompertz constant δ is transcendental.

  6. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number x, one has = ⁡ + ⁡, where e is the base of the natural logarithm, i is the ...

  7. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]

  8. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    Euler's identity is a special case of Euler's formula, which states that for any real number x, e i x = cos ⁡ x + i sin ⁡ x {\displaystyle e^{ix}=\cos x+i\sin x} where the inputs of the trigonometric functions sine and cosine are given in radians .

  9. Gompertz function - Wikipedia

    en.wikipedia.org/wiki/Gompertz_function

    The resulting Gompertz function is for the number of individuals living at a given age as a function of age. ... e is Euler's Number (e = 2. ... is a constant related ...