Ad
related to: eulerian numbers calculator math worksheet answers 3 1
Search results
Results from the WOW.Com Content Network
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 .
The Euler numbers appear in the Taylor series expansions of the secant and hyperbolic secant functions. 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.
3 and each rational prime congruent to 1 mod 3 are equal to the norm x 2 − xy + y 2 of an Eisenstein integer x + ωy. Thus, such a prime may be factored as ( x + ωy )( x + ω 2 y ) , and these factors are Eisenstein primes: they are precisely the Eisenstein integers whose norm is a rational prime.
Euler's great interest in number theory can be traced to the influence of his friend in the St. Peterburg Academy, Christian Goldbach. A lot of his early work on number theory was based on the works of Pierre de Fermat, and developed some of Fermat's ideas. One focus of Euler's work was to link the nature of prime distribution with ideas in ...
hence has Betti number 1 in dimensions 0 and n, and all other Betti numbers are 0. Its Euler characteristic is then χ = 1 + (−1) n ; that is, either 0 if n is odd, or 2 if n is even. The n dimensional real projective space is the quotient of the n sphere by the antipodal map. It follows that its Euler characteristic is exactly half that of ...
Euler numbers, integers occurring in the coefficients of the Taylor series of 1/cosh t; Eulerian numbers count certain types of permutations. Euler number (physics), the cavitation number in fluid dynamics. Euler number (algebraic topology) – now, Euler characteristic, classically the number of vertices minus edges plus faces of a polyhedron.
A perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number n, apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals n, then n is a perfect totient number.
For x = 1, the incomplete beta function coincides with the complete beta function. The relationship between the two functions is like that between the gamma function and its generalization the incomplete gamma function. For positive integer a and b, the incomplete beta function will be a polynomial of degree a + b - 1 with rational coefficients.
Ad
related to: eulerian numbers calculator math worksheet answers 3 1