相关论文: Analytical valuation of some non-elementary integr…
By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3 $, $\Psi_1 $,…
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…
In this paper, we prove two structural theorems on the general Berndt-type integrals with the denominator having arbitrary positive degrees by contour integrations involving hyperbolic and trigonometric functions, and hyperbolic sums…
Minimum divergence estimators provide a natural choice of estimators in a statistical inference problem. Different properties of various families of these divergence measures such as Hellinger distance, power divergence, density power…
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…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
The theory of normal variance mixture distributions is used to provide elementary derivations of closed-form expressions for the definite integrals $\int_0^\infty x^{-2\nu}\cos(bx)\gamma(\nu,\alpha x^2)\,\mathrm{d}x$ (for $\nu>1/2$, $b>0$…
Identification in errors-in-variables regression models was recently extended to wide models classes by S. Schennach (Econometrica, 2007) (S) via use of generalized functions. In this paper the problems of non- and semi- parametric…
The weighted forms of generalized survival and failure entropies of order ($\alpha,\beta$) are proposed and some properties are obtained. We further propose the dynamic versions of weighted generalized survival and failures entropies and…
One-dimensional and two-dimensional integrals containing $E_b(-u)$ and $E_{\alpha ,\beta }\left(\delta x^{\gamma }\right)$ are considered. $E_b(-u)$ is the Mittag-Leffler function and the integral is taken over the rectangle $0 \leq x <…
From the integration of non-symmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. We show that functions characterizing…
In math.QA/0309252, the author proved a number of multivariate elliptic hypergeometric integrals. The purpose of the present note is to explore more carefully the various limiting cases (hyperbolic, trigonometric, rational, and classical)…
We extend the Hanel and Thurner asymptotic analysis to both extensive and non-extensive entropies on the basis of a wide class of entropic forms. The procedure is known to be capable to classify multiple entropy measures in terms of their…
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…
The main object of this paper is to present a new generalized beta function which defined by three parametres Mittag-Leffler function. We also introduce new generalizations of hypergeometric and confluent hypergeometric functions with the…
Let $X_1,X_2, \ldots$ be independent and identically distributed random elements taking values in a separable Hilbert space $\mathbb{H}$. With applications for functional data in mind, $\mathbb{H}$ may be regarded as a space of…
In this paper, we investigate the Euler-type integral representations for the generalized hypergeometric matrix function and develop some transformations in terms of hypergeometric matrix functions. Furthermore, unit and half arguments have…
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…