Related papers: Convolution of beta prime distribution

We obtain so far unproved properties of a ratio involving a class of Hermite and parabolic cylinder functions. Those ratios are shown to be strictly decreasing and bounded by universal constants. Differently to usual analytic approaches, we…

Suppose $\alpha$ is a rotationally symmetric norm on $L^{\infty}\left(\mathbb{T}\right) $ and $\beta$ is a "nice" norm on $L^{\infty}\left(\Omega,\mu \right) $ where $\mu$ is a $\sigma$-finite measure on $\Omega$. We prove a version of…

We consider the set of finite sequences of length n over a finite or countable alphabet C. We consider the function which associate each given sequence with the size of the maximum overlap with a (shifted) copy of itself. We compute the…

We examine two binary operations on the set of algebraic polynomials, known as multiplicative and additive finite free convolutions, specifically in the context of hypergeometric polynomials. We show that the representation of a…

We express generalized Cauchy-Stieltjes transforms of some particular Beta distributions (of ultraspherical type generating functions for orthogonal polynomials) as a powered Cauchy-Stieltjes transform of some measure. For suitable values…

Let $\alpha, \beta \in (0,1)$ such that at least one of them is irrational. We take a random walk on the real line such that the choice of $\alpha$ and $\beta$ has equal probability $1/2$. We prove that almost surely the $\alpha\beta$-orbit…

We present a summation rule using the Mellin transform to give short proofs of some important classical relations between special functions and Bernoulli and Euler polynomials. For example, the values of the Hurwitz zeta function at the…

We compute the exact and limiting smallest eigenvalue distributions for two classes of $\beta$-Jacobi ensembles not covered by previous studies. In the general $\beta$ case, these distributions are given by multivariate hypergeometric…

Let $\A$ be an arrangement of affine lines in $\C^2,$ with complement $\M(\A).$ The (co)homo-logy of $\M(\A)$ with twisted coefficients is strictly related to the cohomology of the Milnor fibre associated to the conified arrangement,…

In investigating the properties of a certain class of homogeneous polynomials, we discovered an identity satisfied by their coefficients which involves simple 2F1 Gauss hypergeometric functions. This result appears to be new and we supply a…

We introduce iterated beta integrals, a new class of iterated integrals on the universal abelian covering of the punctured projective line that unifies hyperlogarithms and classical beta integrals while preserving their fundamental…

This paper describes the quality of convergence to an infinitely divisible law relative to free multiplicative convolution. We show that convergence in distribution for products of identically distributed and infinitesimal free random…

It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function ${}_3F_2$ can be extended to include additional parameter pairs, which differ by integers. In the extended identities,…

We consider a special family of Gaussian hypergeometric functions whose entries are cubic and trivial characters over finite fields. The special values of these functions are known to give the Frobenius traces of families of Hessian…

Recently, the first author as well as the second author with Ono, Pujahari, and Saikia determined the limiting distribution of values of certain finite field ${_2F_1}$ and ${_3F_2}$ hypergeometric functions. These hypergeometric values are…

We show that properties of hypergeometric class equations and functions become transparent if we derive them from appropriate 2nd order differential equations with constant coefficients. More precisely, properties of the hypergeometric and…

Recently it has been shown that the $\alpha$-Sun density $h(x)$ [{\it J. Math. Anal. Appl.}, {\bf 527} (2023), p. 127371] which interpolates between the Fr{\'e}chet density and that of the positive, stable distributions whose density is…

A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…

It is known that the supermultiplet of beta-deformations of ${\cal N}=4$ supersymmetric Yang-Mills theory can be described in terms of the exterior product of two adjoint representations of the superconformal algebra. We present a…

We give a full list of known $\mathcal{N}=1$ supersymmetric quantum field theories related by the Seiberg electric-magnetic duality conjectures for $SU(N), SP(2N)$ and $G_2$ gauge groups. Many of the presented dualities are new, not…