58,931 Results Found

Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that un...

In the present paper, we study the information generating (IG) function and relative information generating (RIG) function measures associated with maximum and minimum ranked set sampling (RSS) schemes with unequal sizes. We also examine the IG measu...

This paper is concerned with the sequence of positive linear operators obtained by certain generating functions of polynomials and with investigation of its approximation properties in detail. Initially, the convergence theorem is expressed for the s...

The aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these ne...

The molecular weight distribution is an important factor that affects the properties of polymers. A control algorithm based on the moment-generating function was proposed to regulate the molecular weight distribution for polymerization processes in t...

In this paper, we introduce and investigate a new subclass of analytic functions in the open unit disk by combining the $(\lambda ,q)$-fractional differintegral operator with the Euler generating function through the technique of subordination. This cl...

Due to the volatile and correlated nature of wind speed, a high share of wind power penetration poses challenges to power system production simulation. Existing power system probabilistic production simulation approaches are in short of considering t...

The Poisson–Three-Parameter Lindley (PTPL) distribution constitutes a flexible Poisson mixture model for overdispersed count data, encompassing several classical count distributions as special or limiting cases. Despite its growing use in appli...

Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-o...

An analytical derivation of the conditional moment-generating function (MGF) for a regime-switching nonlinear drift constant elasticity of variance process is established. The proposed model incorporates both regime-switching mechanisms and nonlinear...

The general quintic functional equation and the general sextic functional equation are generalizations of many functional equations such as the additive function equation and the quadratic function equation. In this paper, we investigate Hyers–...

The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the g...

In this paper, algorithms for calculating different types of generalized trigonometric and hyperbolic functions are developed and presented. The main attention is focused on the Ateb-functions, which are the inverse functions to incomplete Beta-funct...

There are several general concepts that allow obtaining explicit formulas for the coefficients of generating functions in one variable by using their powers. One such concept is the application of compositae of generating functions. In previous studi...

In this paper, we generalize previous results on the generalized stability of the general septic functional equation ${\Delta }_y^{8}f\left(x\right)=0$ for all $x,y\in V$.

Generating functions play important roles in theory of orthogonal polynomials. In particular, it is important to consider generating functions that have symmetry. This paper is a survey on generating functions that define unitary operators. First, cl...

By employing two well-known Euler’s transformations for the hypergeometric function ${}_2{F}_1$, Liu and Wang established numerous general transformation and reduction formulas for the Kampé de Fériet function and deduced many new summati...

Investigation of the generalized trigonometric and hyperbolic functions containing two parameters has been a very active research area over the last decade. We believe, however, that their monotonicity and convexity properties with respect to paramet...

In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcenden...

The generalized trigonometric functions called Ateb-functions are considered. On this basis, a generalization of the Fourier transform is constructed and called the Ateb-transform. From the operator theory point of view, the Ateb-transform is conside...

In this article, we introduce the generalized Bessel–Maitland function (EGBMF) using the extended beta function and some important properties obtained. Thus, we first show interesting relationships of this function with Laguerre polynomials and...

Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. Among them, the Kampé de Fériet function and its generalizations have...

In this paper, we provide a new bivariate distribution obtained from a Kibble-type bivariate gamma distribution. The stochastic representation was obtained by the sum of a Kibble-type bivariate random vector and a bivariate random vector builded by t...

The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we...

In this paper, we study methods for obtaining explicit formulas for the coefficients of generating functions. To solve this problem, we consider the methods that are based on using the powers of generating functions. We propose to generalize the conc...

In the present scenario, coherent states of a quantum harmonic oscillator are generalized with positive Fox H auxiliary functions. The novel generalized coherent states provide canonical coherent states and Mittag-Leffler or Wright generalized cohere...

Demonstrating the striking symmetry between calculus and q-calculus, we obtain q-analogues of the Bateman, Pasternack, Sylvester, and Cesàro polynomials. Using these, we also obtain q-analogues for some of their generating functions. Our q-gen...

Based upon a new general vector-valued vector product, generalized complex numbers with respect to certain positively homogeneous functionals including norms and antinorms are introduced and a vector-valued Euler type formula for them is derived usin...

The objective of this research is to obtain some fractional integral formulas concerning products of the generalized Mittag–Leffler function and two H-functions. The resulting integral formulas are described in terms of the H-function of severa...

In this paper, we consider a generalized Mittag-Leffler (ML)-type function and establish several integral formulas involving Jacobi and related transforms. We also establish some of the composition of generalized fractional derivative formulas associ...

One of the main motivations of this paper is to construct generating functions for generalization of the Touchard polynomials (or generalization exponential functions) and certain special numbers. Many novel formulas and relations for these polynomia...

In the present some generating functions relations of Hermite polynomial also of two, three and in turn several index are derived. Some known and unknown particular cases have also been discussed.

In this paper, we investigate new geometric properties of normalized analytic functions associated with the generalized Marcum Q-function. In particular, we focus on two analytic forms derived from a normalized derivative of a representation involvin...

There are distinct techniques to generate fuzzy implication functions. Despite most of them using the combination of associative aggregators and fuzzy negations, other connectives such as (general) overlap/grouping functions may be a better strategy....

A unifying $\alpha$-parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN) that uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system....

A class of function called sub-b-s-preinvex function is defined as a generalization of s-convex and b-preinvex functions, and some of its basic properties are presented here. The sufficient conditions of optimality for unconstrainded and inquality co...

In this paper, we investigate a general multivariable functional equation. We prove, using the fixed-point method, the generalized Hyers–Ulam stability of this equation in Banach spaces. In this way, we obtain sufficient conditions for the stab...

There have been numerous investigations on the hypergeometric series ${}_2{F}_1$ and the generalized hypergeometric series ${}_p{F}_q$ such as differential equations, integral representations, analytic continuations, asymptotic expansions, reduction cases, extension...

A new subclass of bi-close-to-convex functions associated with the generalized hypergeometric functions defined in ∆$=\{z\in \mathbb{C}:|z|<1\}$ is introduced. The estimates for the general Taylor–Maclaurin coefficients of the functions in the in...

We establish a new identity for generalized hypergeometric functions and apply it for first- and second-kind Gauss summation formulas to obtain some new summation formulas. The presented identity indeed extends some results of the recent published pa...

In this paper, we discussed a new subclass ${\mathcal{J}\mathcal{Q}}_{⅁,A}^B\left(q\right)$ of bi-univalent functions in the unit disk $\mathbb{U}$ using q-generalized Janowski function and q-derivative. Additionally, certain properties were examined and effectively demonstrated, such as the s...

In this paper, we investigate a class of analytic functions associated with the generalized Marcum Q-function and its Alexander transform. We establish sufficient conditions under which these functions exhibit important geometric properties in the op...

The purpose of this article is to give relations among the uniform B-splines, the Bernstein basis functions, and certain families of special numbers and polynomials with the aid of the generating functions method. We derive a relation between generat...

Here, we ascertain generalized integral formulas concerning the product of the generalized Mittag-Leffler function. These integral formulas are described in the form of the generalized Lauricella series. Some special cases are also presented in terms...

In this paper, motivated by the modified Tremblay fractional differential operator and the normalized generalized Bessel–Maitland function, we introduce the generalized Bessel–Maitland–Tremblay function via the Hadamard product tran...

Essentially, whenever a generalized hypergeometric series can be summed in terms of gamma functions, the result will be important as only a few such summation theorems are available in the literature. In this paper, we apply two identities of general...

In existing models with an unknown link function, the issue of predictors containing both multiple functional data and multiple scalar data has not been studied. To fill this gap, we propose a generalized partially functional linear model, which not...

The paper considers the generalized hypergeometric function ${}_{3}F_2,$ which is important in various fields of mathematics, physics, and economics. The method is used, according to which the domains of the analytical continuation of the special f...

Generalization of the ordinary hyperbolic functions called hyperbolic Ateb-functions is considered. They are the inverse of incomplete Beta-function. These functions are solutions of differential equations, which describe the aperiodic vibration moti...

In a number of problems in applied mathematics, physics (theoretical and mathematical), statistics, and other fields the hypergeometric functions of one and several variables naturally appear. Hypergeometric functions in one and several variables hav...