Related papers: Special functions, transcendentals and their numer…
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
This is a survey of results, both classical and recent, on behaviour of plurisubharmonic functions near their $-\infty$-points, together with the related topics for positive closed currents.
We introduce and study new versions of polylogarithms and a zeta function on a completion of $\mathbb F_q (x)$ at a finite place. The construction is based on the use of the Carlitz differential equations for $\mathbb F_q$-linear functions.
We present explicit representations in terms of hypergeometric functions for the scaling functions in the $C^0$ orthogonal multiresolution analyses associated with piecewise continuous polynomials. Closed formulas for the Mellin transform…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…
Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid…
This paper is an enhanced version of a more than decade-older paper with a similar title. Many formulae involving both finite and infinite sums of digamma and polygamma functions up to quadratic order, few of which appear in standard…
We generalize techniques of Addison to a vastly larger context. We obtain integral representations in terms of the first periodic Bernoulli polynomial for a number of important special functions including the Lerch zeta, polylogarithm,…
In this paper we present a new approach to proving some exponential inequalities involving the sinc function. Power series expansions are used to generate new polynomial inequalities that are sufficient to prove the given exponential…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
This paper describes generalized polylogarithms, multiple polylogarithms, and multiple zeta values, along with their implementation in Maple 2018. This set of related functions is of interest in high energy physics as well as in number…
In this paper, we give explicit evaluation for some infinite series involving generalized (alternating) harmonic numbers. In addition, some formulas for generalized (alternating) harmonic numbers will also be derived.
Contents: Generalities, Chiral supermultiplets, Super Yang-Mills theory, Superspace Feynman graphs, Renormalization, Supercurrent, Finite theories.
In this paper, we list several interesting structures of cyclotomic polynomials: specifically relations among blocks obtained by suitable partition of cyclotomic polynomials. We present explicit and self-contained proof for all of them,…
Up-down permutations are counted by tangent resp. secant numbers. Considering words instead, where the letters are produced by independent geometric distributions, there are several ways of introducing this concept; in the limit they all…
We review the results having the property of maximal transcendentality.
The cyclic group labeled family of quasi-projection operators is used for investigation of decomposition of functions with respect to the cyclic group of order n . Series of new identities thus arising are demonstrated and new perspectives…
Some outstanding issues in high energy scattering are discussed. Particular emphasis is placed on recent developments concerning the next-to-leading log corrections to the BFKL equation.