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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 is conjectured not to be an algebraic period, [3] but the values of its first 10 9 decimal digits seem to indicate that it could be a normal number. [ 48 ] Continued fraction

  4. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    The following list includes a decimal expansion and set containing each number, ordered by year of discovery. ... Euler's number [18] 2.71828 18284 ...

  5. 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.

  6. Euler numbers - Wikipedia

    en.wikipedia.org/wiki/Euler_numbers

    The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic secant functions. The latter is the function in the definition. The latter is the function in the definition. They also occur in combinatorics , specifically when counting the number of alternating permutations of a set with an even number of elements.

  7. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    In mathematics, Euler's identity [note 1] (also known as Euler's equation) is the equality + = where e {\displaystyle e} is Euler's number , the base of natural logarithms , i {\displaystyle i} is the imaginary unit , which by definition satisfies i 2 = − 1 {\displaystyle i^{2}=-1} , and

  8. Basel problem - Wikipedia

    en.wikipedia.org/wiki/Basel_problem

    The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]

  9. Transcendental number - Wikipedia

    en.wikipedia.org/wiki/Transcendental_number

    Euler, in the eighteenth century, was probably the first person to define transcendental numbers in the modern sense. [9] Johann Heinrich Lambert conjectured that e and π were both transcendental numbers in his 1768 paper proving the number π is irrational, and proposed a tentative sketch proof that π is transcendental. [10]

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