We define a new kind of classical digamma function, and establish some its fundamental identities. Then we apply the formulas obtained, extend tools developed by Flajolet Salvy to study more general Euler-type sums. The main results Salvy's paper (Expo. Math. 7(1) (1998), 15-35) are immediate corollaries in this paper. Furthermore, provide parameterized extensions Ramanujan-type identities that...

In this paper, the flexural free vibrations of three dimensional micro beams are investigated based on strain gradient theory. The most general form of the strain gradient theory which contains five higher-order material constants has been applied to the micro beam to take the small-scale effects into account. Having considered the Euler-Bernoulli beam model, governing equations of motion are w...

For a collection E of dyadic intervals, a Banach space X, and p ∈ (1, 2] we assume the upper lp estimates

By using Euler-Maclaurin's summation formula and the way of real analysis, a more accurate multipleHilbert-type inequality and the equivalent form are given. We also prove that the same constantfactor in the equivalent inequalities is the best possible.

The protonation of different species of glycylisoleucine were studied in the pH range of 1.5 - 10 at25 °C using potentiometric technique. Investigations were performed in sodium perchlorate andtetraethylammonium iodide as background electrolytes at I (0.1, 0.2, 0.3, 0.4, 0.5, and 0.6) moldm-3. The parameters based on the protonation constants were calculated, and their dependenceson ionic stren...

In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz’s type qBernoulli polynomials and obtained the distribution relation for them. They also raised the following problem: “are there analytic multiple twisted Carlitz’s type q-zeta functions which interpolate multiple twisted Carlitz’s type q-Euler (Bernoulli) polynomials?” The aim of this paper is to give a part...

The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for Re s > 1/2 in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization of the Brauer–Siegel theorem. As an application we obtain a limit formula for Euler–Kronecker constants in families of number fields.

This paper proposes an implementation of a Euler/Venn reasoning system using directed acyclic graphs and shows that this implementation is correct with respect to a modified Shin/Hammer mathematical model of Euler/Venn Reasoning. In proving its correctness it will also be shown that the proposed implementation preserves or inherits the soundness and completeness properties of the mathematical m...