Related papers: Infinite Product of Bicomplex Numbers
Given two infinite sequences with known binomial transforms, we compute the binomial transform of the product sequence. Various identities are obtained and numerous examples are given involving sequences of special numbers: Harmonic…
We give an exact coefficients formula of any infinite product of power series with constant term equal to $1$, by using structures from partitions of integers and permutation groups. This is an universal theorem for various of Binomial-type…
In this article we propose a general method of obtaining infinite sums of products with functions that count patterns in numbers.
We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.
We give an introduction to the theory of Borcherds products and to some number theoretic and geometric applications. In particular, we discuss how the theory can be used to study the geometry of Hilbert modular surfaces.
In this paper the Hochschild-cochain-complex of an A-infinity-algebra A with values in an A-infinity-bimodule M over A and maps between them is defined. Then, an infinity-inner-product on A is defined to be an A-infinity-bimodule-map…
We present new infinite arctangent sums and infinite sums of products of arctangents. Many previously known evaluations appear as special cases of the general results derived in this paper.
Using some basic properties of the gamma function, we evaluate a simple class of infinite products involving Dirichlet characters as a finite product of gamma functions and, in the case of odd characters, as a finite product of sines. As a…
Several infinite products are studied that satisfy the transformation relation of the type $f(\alpha)=f(1/\alpha)$. For certain values of the parameters these infinite products reduce to modular forms. Finite counterparts of these infinite…
In this technical report, certain interesting classification of arithmetical functions is proposed. The notion of additively decomposable and multiplicatively decomposable arithmetical functions is proposed. The concepts of arithmetical…
By treating the multiple argument identity of the logarithm of the Gamma function as a functional equation, we obtain a curious infinite product representation of the $sinc$ function in terms of the cotangent function. This result is…
We study an infinite countable iteration of the natural product between ordinals. We present an "effective" way to compute this countable natural product, in the non trivial cases the result depends only on the natural sum of the degrees of…
A construction of product measures is given for an arbitrary sequence of measure spaces via outer measure techniques without imposing any condition on the underlying measure spaces. This approach concludes finally the problem of the…
We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that…
The regularized product of the Fibonacci numbers is evaluated.
If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.
The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments…
We study several integrals that contain the infinite product ${\displaystyle\prod_{n=0}^\infty}\left[1+\left(\frac{x}{b+n}\right)^3\right]$ in the denominator of their integrand. These considerations lead to closed form evaluation…
We show how to define biproducts up to isomorphism in an arbitrary category without assuming any enrichment. The resulting notion coincides with the usual definitions whenever all binary biproducts exist or the category is suitably…
Two kinds of infinite product representations for Vign\'eras multiple gamma function are presented. As an application of these formulas, a multiplication formula for the function is derived.