Related papers: The beta function of a knot
An analogue of Brylinski's knot beta function is defined for a submanifold of d-dimensional Euclidean space. This is a meromorphic function on the complex plane. The first few residues are computed for a surface in three dimensional space.
An analogue of Brylinski's knot beta function is defined for a compactly supported (Schwartz) distribution $T$ on $d$-dimensional Euclidean space. This is a holomorphic function on a right half-plane. If $T$ is a (uniform) double-layer on a…
Motivated by the integral representation of the Euler Beta function, we introduce its Cauchy siblings and investigate some of their properties. Two of these newly introduced functions happen to coincide with some classical means, such as…
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…
The table of Gradshteyn and Rhyzik contains some trigonometric integrals that can be expressed in terms of the beta function. We describe the evaluation of some of them.
In [Pooja Rani and M. K. Vemuri, The Brylinski beta function of a double layer, Differential Geom. Appl. \textbf{92}(2024)], an analogue of Brylinski's knot beta function was defined for a compactly supported (Schwartz) distribution $T$ on…
Israel M. Gelfand gave a geometric interpretation for general hypergeometric functions as sections of the tautological bundle over a complex Grassmannian $G_{k,n}$. In particular, the beta function can be understood in terms of $G_{2,3}$.…
We define Bernstein-Sato polynomials for meromorphic functions and study their basic properties. In particular, we prove a Kashiwara-Malgrange type theorem on their geometric monodromies, which would be useful also in relation with the…
In this paper, we introduce and investigate a new extension of the beta function by means of an integral operator involving a product of Bessel-Struve kernel functions. We also define a new extension of the well-known beta distribution, the…
This short note deals with some applications of the Beta function
The classical beta function B(x; y) is one of the most fundamental special functions, due to its important role in various fields in the mathematical, physical, engineering and statistical sciences. Useful extensions of the classical Beta…
We provide constructions of bent functions using triples of permutations. This approach is due to Mesnager. In general, involutions have been mostly considered in such a machinery; we provide some other suitable triples of permutations,…
Using a probabilistic approach, we derive several interesting identities involving beta functions. Our results generalize certain well-known combinatorial identities involving binomial coefficients and gamma functions.
Let $\alpha$ be a map from the set of all knot types ${\mathcal K}$ to a set $X$. Let $\beta$ be a map from ${\mathcal K}$ to a set $Y$. We define the relation between $\alpha$ and $\beta$ to be the image of a map $(\alpha,\beta)$ from…
The signature function of a knot is an integer-valued step function on the unit circle in the complex plane. Necessary and sufficient conditions for a function to be the signature function of a knot are presented.
Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the beta-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
We derive the full set of beta functions for the marginal essential couplings of projectable Horava gravity in (3 + 1)-dimensional spacetime. To this end we compute the divergent part of the one-loop effective action in static background…
We study the beta functions for the dimensionless couplings in quadratic curvature gravity, and find that there is a simple argument to restrict the possible form of the beta functions as derived from the counterterms at an arbitrary loop.…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…