Anthony Sofo

In this paper, we study certain classes of nested logarithmic integrals called Malmsten integrals and generalize certain results obtained by Blagouchine. These nested logarithmic integrals yield solutions in terms of sums of odd Riemann zeta and even Dirichlet beta values. We establish that the coefficients of these sums involve the central factorial numbers. Moreover, we provide an alternative proof for the expression of single instances of these values by means of the Eulerian polynomials and their midpoint variant. Finally, we derive consequences of these identities by making use of their self reciprocal properties. We thus establish a novel representation for the Midpoint Eulerian polynomials.

The exploration of linear Euler harmonic sums had its beginnings with the works of Euler in the 18th century. In 1998 Flajolet and Salvy published a seminal paper in which they developed an approach to the evaluation of linear Euler harmonic sums and gave explicit formulae for several classes of Euler sums in terms of Riemann zeta and other special function values. In this paper, results given by Flajolet and Salvy are extended and generalized.

We develop a number of new identities for linear Euler harmonic number sums with multiple argument. Some new examples of even weight linear Euler harmonic sum identities are given.

In this paper we investigate a class of integrals that were encountered in the course of a work on statistical plasma physics, in the so-called Sommerfeld temperature-expansion of the electronic entropy. We show that such integrals, involving some parameters, can be fully described in closed form represented by special functions.

In this paper we investigate a class of integrals that were encountered in the course of a work on statistical plasma physics, in the so-called Sommerfeld temperature-expansion of the electronic entropy. We show that such integrals, involving some parameters, can be fully described in closed form represented by special functions.

We investigate the linear arrangement of Euler harmonic sums that may be expressed in closed form in terms of special functions such as the classical Riemann zeta function and the Dirichlet eta function. Particular emphasis is given to Euler harmonic sums with even weight. New examples highlighting the theorems will be presented.

In this study we investigate a family of skew linear harmonic Euler sums involving some free parameters. Our analysis involves using the properties of the polylogarithm function, commonly referred to as the Bose-Einstein integral. A reciprocity property is utilized to highlight an explicit representation for a particular skew harmonic linear Euler sum. A number of examples are also given which highlight the theorems. This work generalizes some results in the published literature and introduces some new results.