Related papers: On a multiple harmonic power series
This work is a sequel of a previous work of one of the authors (Y.\^O), which treated certain congruence relation between an elliptic Gauss sum and a coefficient of power series expansion at the origin of the lemniscate sine function. We…
Based on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived. A high point of the…
We consider real non-symmetric matrices and their factorisation as a product of real symmetric matrices. The number of complex eigenvalues of the original matrix reveals restrictions on such factorisations as we shall prove.
We obtained the region of convergence and the summation formula for some modified generalized hypergeometric series (1.2). We also investigated rationality of the sums of the power series (1.3). As a result the series (1.4) cannot be the…
After a systematic introduction of some formulae for the energy radiated by localized electric charges and currents, one considers the multipole radiation and the reduction of the multipole tensors to the symmetric traceless ones.
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series…
A new formula for the heavy quark-antiquark spin dependent potential is given by using the techniques developed in the heavy quark effective theory. The leading logarithmic quark mass terms emerging from the loop contributions are…
In this paper, based on the weak form of the Hamiltonian formulation of the regularized long-wave equation and a novel approach of transforming the original Hamiltonian energy into a quadratic functional, a fully implicit and three…
The issue of consistent power counting in baryon chiral perturbation theory is revisited.
A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.
A general integral expression to transform power series is applied to $\arcsin{x}$ and its positive integer powers. We concentrate on the first to the fourth powers and obtain infinite classes of new power series involving central binomial…
Recently published formulas for the surface and regular solid spherical harmonics and for the expansion of the product of two normalized associated Legendre functions with different centers in ellipsoidal coordinates (Telhat Ozdogan, Metin…
In this note, we give examples of formal power series satisfying certain conditions that cannot be realized as Hilbert series of finitely generated modules. This answers to the negative a question raised in a recent article by the second…
In this work we develop some fifth-order integrable coupled systems of weight $0$ and $1$ which possess seventh-order symmetry. We establish four new systems, where in some cases, related recursion operator and bi-Hamiltonian formulations…
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
In this paper, we intend to revisit Theorem 2 of [3] formulating it in a way that, weakening the hypotheses and, at the same time, highlighting the richer conclusion allowed by the proof, it can potentially be applicable to a broader range…
We introduce notions of bi-unitary, bi*-unitary and bi**-unitary harmonic numbers, along with their preliminary study.
In previous works, we presented series representations for $\pi^3$ and $\pi^5$, in which the prefactor depends only on the golden ratio appears. In this article, we derive a general relation involving trigonometric functions and an infinite…
The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and…