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2. 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.

3. 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 .

4. 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.

5. Proof that e is irrational - Wikipedia

   en.wikipedia.org/wiki/Proof_that_e_is_irrational

   The number e was introduced by Jacob Bernoulli in 1683. More than half a century later, Euler, who had been a student of Jacob's younger brother Johann, proved that e is irrational; that is, that it cannot be expressed as the quotient of two integers.

6. Euler's constant - Wikipedia

   en.wikipedia.org/wiki/Euler's_constant

   Using the same approach, in 2013, M. Ram Murty and A. Zaytseva showed that the generalized Euler constants have the same property, [3] [44] [45] where the generalized Euler constant are defined as = (= ⁡ = ()), where ⁠ ⁠ is a fixed list of prime numbers, () = if at least one of the primes in ⁠ ⁠ is a prime factor of ⁠ ⁠, and ...

7. Eulerian number - Wikipedia

   en.wikipedia.org/wiki/Eulerian_number

   In combinatorics, the Eulerian number (,) is the number of permutations of the numbers 1 to in which exactly elements are greater than the previous element (permutations with "ascents"). Leonhard Euler investigated them and associated polynomials in his 1755 book Institutiones calculi differentialis .