相关论文: The Ehrhart Function for Symbols
In this paper, we derive the quadratic formula as a consequence of constructively proving the existence of standard and factored forms for general form real quadratic functions. Emphasis is put on connections to graphing of corresponding…
We show that there exists a fixed recursive function $e$ such that for all functions $h\colon \mathbb{N}\to \mathbb{N}$, there exists an injective function $c_h\colon \mathbb{N}\to \mathbb{N}$ such that $c_h(h(n))=e(c_h(n))$, i.e.,…
As a function of second variable, we identify the Fourier series of Hurwitz zeta function and its derivatives on the unit interval. Consequently, we obtain results based on the formula for Fourier coefficients and also on Parseval's…
In the present paper, we were mainly concerned with obtaining estimates for the general Taylor-Maclaurin coefficients for functions in a certain general subclass of analytic bi-univalent functions. For this purpose, we used the Faber…
In this paper, basing on the linear algebra methods and elementary techniques, for any positive integers $ e $ and $ n $, we obtain a recursion formula for the generalized Euler function $ \varphi_e(n) $, which is determined by some…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
In this note, we give an alternative proof of the generating function of $p$-Bernoulli numbers. Our argument is based on the Euler's integral representation.
In this paper, by using the orthogonality type as defined in the umbral calculus, we derive explicit formula for several well known polynomials as a linear combination of the Apostol-Euler polynomials.
In this paper, we derive by using elementary methods some continued fractions, certain identities involving derivatives of tanx, several expressions for log coshx and an identity for {\pi}2, from a series expansion of tan x, which gives the…
This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional…
By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on $\mathcal{H}^2$, the space of Dirichlet series with square summable coefficients, for the inducing symbol $\varphi(s)=c_1+c_{q}q^{-s}$…
In the present work, by taking advantage of a so-called practical limitation of fractional derivatives, namely, the absence of a simple chain and Leibniz's rules, we proposed a generalized fractional calculus of variation where the…
This short note provides an explicit description of the Fr\'echet derivatives of the principal square root matrix functional at any order. We present an original formulation that allows to compute sequentially the Fr\'echet derivatives of…
In this short paper, we derive an integral representation for Euler sums of hyperharmonic numbers. We use results established by other authors to then show that the integral has a closed-form in terms of zeta values and Stirling numbers of…
We introduce a natural method of computing antiderivatives of a large class of functions which stems from the observation that the series expansion of an antiderivative differs from the series expansion of the corresponding integrand by…
We give yet another proof for Fa\`{a} di Bruno's formula for higher derivatives of composite functions. Our proof technique relies on reinterpreting the composition of two power series as the generating function for weighted integer…
The image of Euler's totient function is composed of the number 1 and even numbers. However, many even numbers are not in the image. We consider the problem of finding those even numbers which are in the image and those which are not. If an…
The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.
We derive an efficient algorithm to find solutions to Euler's concordant form problem and rational points on elliptic curves associated with this problem.
A generalization of the Wigner function for the case of a free particle with the ``relativistic'' Hamiltonian $\sqrt{{\bf p}^2+m^2}$ is given.