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We derive some series related to the polylogarithmic function, and we also give a new proof to the existing series. Our approach is based on using the summation and integral representation methods. We obtain various interesting series as a consequence.

We derive some series related to the polylogarithmic function, and we also give a new proof to the existing series. Our approach is based on using the summation and integral representation methods. We obtain various interesting series as a consequence

We derive some series related to the polylogarithmic function, and we also give a new proof to the existing series. Our approach is based on using the summation and integral representation methods. We obtain various interesting series as a consequence.

We derive some series related to the polylogarithmic function, and we also give a new proof to the existing series. Our approach is based on using the summation and integral representation methods. We obtain various interesting series as a consequence.

We study the well-known lacunary sums of binomial coefficients considered, most notably, by Christian Ramus, and their connection to a special kind of harmonic number associated with the first case of Fermat's Last Theorem. For one case of Ramus's famous identity we obtain a variation in which some of the parameters are replaced by square matrices of arbitrary dimension.

We study the well-known lacunary sums of binomial coefficients considered, most notably, by Christian Ramus, and their connection to a special kind of harmonic number associated with the first case of Fermat's Last Theorem. For one case of Ramus's famous identity we obtain a variation in which some of the parameters are replaced by square matrices of arbitrary dimension.

Three new closed-form summation formulae involving harmonic numbers are established using simple arguments and they are very general extensions of Eulers famous harmonic sum identity. Some illustrative special cases as well as immediate consequences of the main results are also considered.

Three new closed-form summation formulae involving harmonic numbers are established using simple arguments and they are very general extensions of Eulers famous harmonic sum identity. Some illustrative special cases as well as immediate consequences of the main results are also considered.

In a recent paper Dattoli and Srivastava [3], by resorting to umbral calculus, conjectured several generating functions involving harmonic numbers. In this sequel to their work our aim is to rigorously demonstrate the truth of the Dattoli-Srivastava conjectures by making use of simple analytical arguments. In addition, one of these conjectures is stated and proved in more general form. (C) 2009 Elsevier Inc. All rights reserved.

In a recent paper Dattoli and Srivastava [3], by resorting to umbral calculus, conjectured several generating functions involving harmonic numbers. In this sequel to their work our aim is to rigorously demonstrate the truth of the Dattoli-Srivastava conjectures by making use of simple analytical arguments. In addition, one of these conjectures is stated and proved in more general form. (C) 2009 Elsevier Inc. All rights reserved.

In joint work Robin Pemantle and I (2004) consider a doubly infinite sum which is not equal to 1, as first suspected, but evaluates to a sum of products of values of the zeta function. Subsequently, I report on this project.