Related papers: Some applications of the Beta function

We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as well as hypergeometric functions are presented. Several…

In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the…

Several sets of quaternionic functions are described and studied. Residue current of the right inverse of a quaternionic function is introduced in particular cases.

Several new applications of Katona's circle are given.

We study a scalar field theory coupled to gravity on a flat background, below Planck's energy. Einstein's theory is treated as an effective field theory. Within the context of Wilson's renormalization group, we compute gravitational…

Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the \emph{moment zeta function} of a probability distribution, and study in depth some asymptotic properties…

In this paper, we investigate new relationships for bilateral series related to two-parameter mock theta functions, which lead to many identities concerning the bilateral mock theta functions. In addition, interesting relations between the…

This short report details the mathematical properties of the stretched exponential function and some of its applications in materials science. G(tau) distributions for different values of the stretching parameter beta are provided.

In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.

Best present experimental achievements in double beta decay are presented. Possible progress in this field in the near and far future is discussed.

In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.

This paper discusses the incomplete Gamma and Beta integrals involving the generalised hypergeometric function. The distribution of the largest and the smallest roots of a ratio arising in comparing the mean differences among groups is…

The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of Beta function recently defined by Shadab et al.[19]. Moreover, we establish some results related to the newly…

Analyzing in detail the analytic continuation of the Riemann zeta function we are able to generate several new identities which may be useful for application in physics and mathematics.

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…

Properties of the beta functions are investigated. We define the generalized arcsine probability distribution with bounded support. The properties of the beta functions prove some results for this distribution.

Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central…

We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to areas related to partial sums of powers. We apply these…

The table of Gradshteyn and Ryzhik contains some integrals that can be expressed in terms of the incomplete beta function. We describe some elementary properties of this function and use them to check some of the formulas in the mentioned…

In this paper, we present some double inequalities involving certain ratios of the Gamma function. These results are further generalizations of several previous results. The approach is based on the monotonicity properties of some functions…