Related papers: Notes on the historical bibliography of the gamma …
Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…
By using the theory of the elliptic integrals a new method of summation is proposed for a certain class of series and their derivatives involving hyperbolic functions. It is based on the termwise differentiation of the series with respect…
We evaluate binomial series with harmonic number coefficients, providing recursion relations, integral representations, and several examples. The results are of interest to analytic number theory, the analysis of algorithms, and…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
Recent progress in analytical calculation of the multiple [inverse, binomial, harmonic] sums, related with epsilon-expansion of the hypergeometric function of one variable are discussed.
We show that an apparently overlooked result of Euler from \cite{E421} is essentially equivalent to the general multiplication formula for the $\Gamma$-function that was proven by Gauss in \cite{Ga28}.
The present technical notes offer a brief summary of the essential points of electromagnetism at the undergraduate physics level. Some problems are presented at the end of each section; those with solutions are marked with an asterisk.
In this paper we study the integral of type \[_{\delta,a}\Gamma_{\rho,b}(x) =\Gamma(\delta,a;\rho,b)(x)=\int_{0}^{\infty}t^{x-1}e^{-\frac{t^{\delta}}{a}-\frac{t^{-\rho}}{b}}dt.\] Different authors called this integral by different names…
In this paper, we consider the generating functions of the complete and elementary symmetric functions and provide a new generalization of these classical symmetric functions. Some classical relationships involving the complete and…
Tentative analysis of alternative peer review and journal models. Open Access and Impact factor issues are not covered. The bibliography, in alphabetical order, lists articles and web sites (with brief description).
This paper is a set of notes that we wrote concerning the first version of Emergent Gravity [gr-qc/0602022]. It is our version of an exercise that we proposed to some of our students. The idea was to find mathematical errors and…
A table of sums useful for generating function applications (discrete Laplace transforms or z-transforms). Related definitions and formulas (including Lagrange's expansion), and reference to formulas in Abramowitz and Stegun, Handbook of…
This work proposes an algebraic model for classical information theory. We first give an algebraic model of probability theory. Information theoretic constructs are based on this model. In addition to theoretical insights provided by our…
Recently, several new results related to the evaluation of the series sum (-1)^n zeta(n)/(n+k) were published. In this short note we show that this series also possesses an interesting connection to the values of the zeta-function on the…
Special functions and their applications in quantum mechanics and electromagnetism: Course notes.
We give an informal survey of the historical development of computations related to prime number distribution and zeros of the Riemann zeta function.
We derive new reduction formulas for the incomplete beta function and the Lerch transcendent in terms of elementary functions. As an application, we calculate some new integrals. Also, we use these reduction formulas to test the performance…
Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An…
Real analytic generalized functions are investigated as well as the analytic singular support and analytic wave front of a generalized function in $\mathcal{G}(\Omega)$ are introduced and described.
This is a list of corrections for the book: J. Noguchi and T. Ochiai, Geometric Function Theory in Several Complex Variables, xi + 282 pp., Math.\ Monographs Vol.\ {\bf 80}, Amer.\ Math.\ Soc., Providence, 1990. The authors hope that this…