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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. List of representations of e - Wikipedia

    en.wikipedia.org/wiki/List_of_representations_of_e

    A unique representation of e can be found within the structure of Pascal's Triangle, as discovered by Harlan Brothers. Pascal's Triangle is composed of binomial coefficients, which are traditionally summed to derive polynomial expansions. However, Brothers identified a product-based relationship between these coefficients that links to e.

  4. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    The number e (e = 2.718...), also known as Euler's number, which occurs widely in mathematical analysis The number i , the imaginary unit such that i 2 = − 1 {\displaystyle i^{2}=-1} The equation is often given in the form of an expression set equal to zero, which is common practice in several areas of mathematics.

  5. Euler's formula - Wikipedia

    en.wikipedia.org/wiki/Euler's_formula

    Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics". [2] When x = π, Euler's formula may be rewritten as e iπ + 1 = 0 or e iπ = −1, which is known as Euler's identity.

  6. Greek letters used in mathematics, science, and engineering

    en.wikipedia.org/wiki/Greek_letters_used_in...

    a symbol for psychology; the wave function in the Schrödinger equation of quantum mechanics; represents: the J/psi mesons in particle physics; the stream function in fluid dynamics; the reciprocal Fibonacci constant; the second Chebyshev function in number theory; the polygamma function in mathematics; the supergolden ratio [8]

  7. Exponential function - Wikipedia

    en.wikipedia.org/wiki/Exponential_function

    Exponential functions with bases 2 and 1/2. In mathematics, the exponential function is the unique real function which maps zero to one and has a derivative equal to its value. . The exponential of a variable ⁠ ⁠ is denoted ⁠ ⁡ ⁠ or ⁠ ⁠, with the two notations used interchangeab

  8. Expected value - Wikipedia

    en.wikipedia.org/wiki/Expected_value

    According to this definition, E[X] exists and is finite if and only if E[X +] and E[X −] are both finite. Due to the formula |X| = X + + X −, this is the case if and only if E|X| is finite, and this is equivalent to the absolute convergence conditions in the definitions above. As such, the present considerations do not define finite ...

  9. Mathematical notation - Wikipedia

    en.wikipedia.org/wiki/Mathematical_notation

    The international standard ISO 80000-2 (previously, ISO 31-11) specifies symbols for use in mathematical equations. The standard requires use of italic fonts for variables (e.g., E = mc 2 ) and roman (upright) fonts for mathematical constants (e.g., e or π).