相关论文: Elementary evaluations of some Euler sums

Equivalencies of many basic elementary inequalities are given

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

Relations among integrals of logarithms, polylogarithms and Euler sums are presented. A unifying element being the introduction of Nielsen's generalized polylogarithms.

This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.

Lectures notes (in italian) of some arguments of classical analysis, with exercises. A particular emphasis to functional analysis and elementary operator algebra theory is given, by means of exercises and examples.

We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions,…

In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta…

These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.

A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.

In this note, we propose simple summations for primes, which involve two finite nested sums and Bernoulli numbers. The summations can also be expressed in terms of Bernoulli polynomials.

This short note delivers, via elementary calculations, a product representation of pi.

In this paper, we study the alternating Euler $T$-sums and related sums by using the method of contour integration. We establish the explicit formulas for all linear and quadratic Euler $T$-sums and related sums. Some interesting new…

This note presents a rather intuitive approach to extreme value theory. This approach was devised mostly for pedagogical reason.

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…

We present a large number of analytic evaluations of Euler sums, namely sums such as \begin{align} M(m,n_0,n_1,n_2, \ldots, n_t) &= \sum_{k=1}^\infty \frac{H(k)^m}{k^{n_0} (k+1)^{n_1} (k+2)^{n_2} \cdots (k+t)^{n_t}}, \nonumber \end{align}…

We give a completely elementary study for averages of short correlations of so-called sieve functions (a pretty general class of arithmetic functions).

Estimates of some integrals related to variations of smooth functions are presented.

This note gives a simple approach to q-analogues of some results associated with Abel polynomials.

In this paper we find the partial sums of two kinds normalized Wright functions and the partial sums of Alexander transform of these normalized Wright functions.

Lecture notes for an introductory course in elementary particles.