Related papers: Some fascinating series and their sums
Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the…
Several methods are used to evaluate finite trigonometric sums. In each case, either the sum had not previously been evaluated, or it had been evaluated, but only by analytic means, e.g., by complex analysis or modular transformation…
In this paper we consider a transformation $L_a$ of sequences of complex numbers. We find the inverse transformation of $L_a$ as well as the inverse of a related transformation $\tilde{L}_a$. We explore a connection to the binomial…
This paper offers a solution method that allows one to find exact values for a large class of convergent series of rational terms. Sums of this form arise often in problems dealing with Quantum Field Theory.
The main purpose of this paper is to establish some new properties of Horadam numbers in terms of binomial sums. By that, we can obtain these special numbers in a new and direct way. Moreover, some connections between Horadam and…
We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.
We derive some, seemingly new, curious additive relations in the Pascal triangle. They arise in summing up the numbers in the triangle along some vertical line up to some place.
An algebraic framework in which to study infinite sums is proposed, complementing and augmenting the usual topological tools. The framework subsumes numerous examples in the literature. It is developed using many varied examples, with a…
In this article we shows some results about algebra with the group of units having special polynomial identity.
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend some properties of Bernoulli polynomials and numbers such…
The aim of this paper is to provide a new class of series identities in the form of four general results. The results are established with the help of generalizatons of the classical Kummer's summation theorem obtained earlier by Rakha and…
We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.
In this paper, a time series model with coefficients that take values from random matrix ensembles is proposed. Formal definitions, theoretical solutions, and statistical properties are derived. Estimation and forecast methodologies for…
First we survey generating function methods for obtaining useful probability estimates about random matrices in the finite classical groups. Then we describe a probabilistic picture of conjugacy classes which is coherent and beautiful.…
The present note considers a certain family of sums indexed by the set of fixed length compositions of a given number. The sums in question cannot be realized as weighted compositions. However they can be be related to the hypergeometric…
In this paper, a new method for generation of infinite series of symmetric identities written for exponential sums in real numbers is proposed. Such systems have numerous applications in theory of numbers, chaos theory, algorithmic…
By systematically applying ten well-known and inequivalent two-part relations between hypergeometric sums 3F2(...|1) to the published database of all such sums, 62 new sums are obtained. The existing literature is summarized, and many…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
We extend several celebrated methods in classical analysis for summing series of complex numbers to series of complex matrices. These include the summation methods of Abel, Borel, Ces\'aro, Euler, Lambert, N\"orlund, and Mittag-Leffler,…