Euler–frobenius Numbers and Rounding
نویسنده
چکیده
We study the Euler–Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this is more or less implicit in various results and we try to explain this and various connections to other areas of mathematics, such as spline theory. The mean, variance and (some) higher cumulants of the distribution are calculated. Asymptotic results are given. We include a couple of applications to rounding errors and election methods.
منابع مشابه
Viewing Some Ordinary Differential Equations from the Angle of Derivative Polynomials
In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.
متن کاملOn the Explicit Formula of Euler Numbers and Polynomials of Higher Order
In [1], the multiple Frobenius-Euler numbers and polynomials were constructed. In this paper we give some interesting formulae which are related to the multiple Frobenius-Euler polynomials. The main purpose of this paper is to give the Kummer type congruences for the multiple Frobenius-Euler numbers. §
متن کاملGenerating Functions for q-Apostol Type Frobenius-Euler Numbers and Polynomials
The aim of this paper is to construct generating functions, related to nonnegative real parameters, for q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius–Euler polynomials and numbers). We derive some identities for these polynomials and numbers based on the generating functions and functional equations. We also give multiplication formula for the generalized Apostol type Fro...
متن کاملAN IDENTITY OF THE SYMMETRY FOR THE FROBENIUS-EULER POLYNOMIALS ASSOCIATED WITH THE FERMIONIC p-ADIC INVARIANT q-INTEGRALS ON Zp
Abstract. The main purpose of this paper is to prove an identity of symmetry for the Frobenius-Euler polynomials. It turns out that the recurrence relation and multiplication theorem for the Frobenius-Euler polynomials which discussed in [ K. Shiratani, S. Yamamoto, On a p-adic interpolation function for the Euler numbers and its derivatives, Memo. Fac. Sci. Kyushu University Ser.A, 39(1985), 1...
متن کاملq-EULER AND GENOCCHI NUMBERS
Carlitz has introduced an interesting q-analogue of Frobenius-Euler numbers in [4]. He has indicated a corresponding Stadudt-Clausen theorem and also some interesting congruence properties of the q-Euler numbers. In this paper we give another construction of q-Euler numbers, which are different than his q-Euler numbers. By using our q-Euler numbers, we define the q-analogue of Genocchi numbers ...
متن کامل