Abstract. If {an}n=1 and {bn}n=1 are two sequences such that a1 = b1 and bn + a1bn−1 + · · ·+ an−1b1 = nan (n > 1), then we say that (an, bn) is a Newton-Euler pair. In the paper we establish many formulas for Newton-Euler pairs, and then make use of them to obtain new results concerning some special sequences such as p(n), σ(n) and Bn, where p(n) is the number of partitions of n, σ(n) is the s...

We study a q-logarithm which was introduced by Euler and give some of its properties. This q-logarithm did not get much attention in the recent literature. We derive basic properties, some of which were already given by Euler in a 1751-paper and 1734-letter to Daniel Bernoulli. The corresponding q-analogue of the dilogarithm is introduced. The relation to the values at 1 and 2 of a q-analogue o...

The main purpose of this paper is to derive various Matiyasevich-Miki-Gessel type convolution identities for Bernoulli and Genocchi polynomials and numbers by applying some Euler type identities with two parameters.

For linear partial differential equations, there exist well-developed classical methods of their analytical solution, which, in particular, includes the separation of variables, different integral transforms, Fourier series and their generalizations. At the same time, the study of symmetry properties of such equations is important, first of all, for the development of methods of symmetry analys...

Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generali...

Athermal random fiber networks are usually modeled by representing each fiber as a truss, a Euler-Bernoulli or a Timoshenko beam, and, in the case of cross-linked networks, each cross-link as a pinned, rotating, or welded joint. In this work we study the effect of these various modeling options on the dependence of the overall network stiffness on system parameters. We conclude that Timoshenko ...