Related papers: Lost in the Log-Polynomial Expansion: Comment on a…
In the paper [Hong-Shi Zong, Wei-Min Sun, Phys. Lett. B 640 (2006) 196], the authors claim that our proof of the inconsistency of the ladder approximation to QCD [Phys. Lett. B 611 (2005) 129] was incorrect. However, their claim is based on…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
We show how one can obtain rational approximants for $q$-extensions of the harmonic series and the logarithm (and many other similar quantities) by Pad\'e approximation using little $q$-Legendre polynomials and we show that properties of…
The classical orthogonal polynomials (Hermite, Laguerre and Jacobi) are involved in a vast number of applications in physics and engineering. When large degrees $n$ are needed, the use of recursion to compute the polynomials is not a good…
Risaliti, Lusso \& collaborators have constructed a high-redshift Hubble diagram of supernovae (SNe); quasars (QSO) and gamma-ray bursts (GRB) that shows a "$\sim 4 \, \sigma$ tension with the $\Lambda$CDM model" based on a log polynomial…
In the 90's a collection of Plethystic operators were introduced in [3], [7] and [8] to solve some Representation Theoretical problems arising from the Theory of Macdonald polynomials. This collection was enriched in the research that led…
In arXiv:2505.18900 it was claimed that an apparent evolution of the dark energy equation of state occurs within the standard $\Lambda$CDM cosmological model. I point out that this erroneous conclusion is due to a mathematical error.
Majorization inequalities for symmetric polynomials have interested mathematicians for centuries, from the AM-GM inequality for two variables going back at least to Euclid, through classical results of Newton, Muirhead and Gantmacher, to…
We introduce the relation ${\rho}_{\lambda}$-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives, and present some of its essential properties. Among other things, we give…
In recent postings, Foreman & Scott and Gnedin criticize my work on the baryonic Tully-Fisher relation (BTFR) of gas rich galaxies as tests of MOND and LCDM (McGaugh 2011a,b). These criticisms are rather redundant, as they mostly rehash…
Motivated by several conjectures posed in the paper "F. Qi and A.-Q. Liu, Completely monotonic degrees for a difference between the logarithmic and psi functions, J. Comput. Appl. Math., vol. 361, pp. 366--371 (2019); available online at…
We present two new classes of orthogonal functions, log orthogonal functions (LOFs) and generalized log orthogonal functions (GLOFs), which are constructed by applying a $\log$ mapping to Laguerre polynomials. We develop basic approximation…
In this paper we obtain the formal asymptotic expansion of the logarithms $\ln p_s(\alpha)$ of $p_s(\alpha)$, which are canonical continuations of polynomials of binomial type $p_n(\alpha)$. Our approach is based on linear methods which do…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
Approximations for an unknown density $g$ in terms of a reference density $f_\nu$ and its associated orthonormal polynomials are discussed. The main application is the approximation of the density $f$ of a sum $S$ of lognormals which may…
The paper [1] by Liu, Madhavan, and Tegmark sought to use machine learning methods to elicit known conservation laws for several systems. However, in their example of a damped 1D harmonic oscillator they made seven serious errors, causing…
This paper revisits the notion of classical orthogonal polynomials from a broader functional-analytic point of view. It is intended neither as a survey of known results nor as a review of the literature, but rather as a conceptual…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
The LCDM cosmological model assumes the existence of a small cosmological constant in order to explain the observed accelerating cosmic expansion. Despite the dramatic improvement of the quality of cosmological data during the last decade…
This brief note corrects some errors in the paper quoted in the title, highlights a combinatorial result which may have been overlooked, and points to further improvements in recent literature.