353,625 Results Found

Two theories that align with and support Usage-based approaches to language acquisition are Functionalism, which motivates the communicative functions of form-meaning connections produced by grammatical phenomena, and Connectionism, which provides a...

We calculate some infinite sums containing the digamma function in closed form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as parameter...

The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representation...

In this study, we introduce the new subclasses, ${\mathcal{M}}_{\alpha }(sin)$ and ${\mathcal{M}}_{\alpha }(cos)$, of $\alpha$-convex functions associated with sine and cosine functions. First, we obtain the initial coefficient bounds for the first five coefficients of the functions t...

The choice of the activation functions in neural networks (NN) are of paramount importance in the training process and the performance of NNs. Therefore, the machine learning community has directed its attention to the development of computationally...

Let $\mathcal{P}$ be a system of generalized prime numbers, and ${\mathcal{N}}_{\mathcal{P}}$ the corresponding system of generalized integers. Assuming that ${\displaystyle \underset{m\in {\mathcal{N}}_{\mathcal{P}}}{{\displaystyle \sum _{m⩽x}}}}1-ax\ll x^{\beta }$ with $a>0$ and $0⩽\beta <1$, we consider the Beurling zeta-function ${\mathrm{\&zeta}}_{}$...

In this paper, we discuss two well-known coefficient functionals $a_2{a}_4-{a_3}^2$ and $a_4-a_2{a}_3$ . The first one is called the Hankel determinant of order 2. The second one is a special case of Zalcman fun...

This paper shows that certain ${}_{3}F_4$ hypergeometric functions can be expanded in sums of pair products of ${}_{1}F_2$ functions. In special cases, the ${}_{3}F_4$ hypergeometric functions reduce to ${}_{2}F_3$ functions. Further special cases allow one to reduce the ${}_{2}F_3$ functi...

The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transf...

In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functi...

We consider the functional Hamilton–Jacobi (HJ) equation, which is the central equation of the holographic renormalization group (HRG), functional Schrödinger equation, and generalized Wilson–Polchinski (WP) equation, which is the ce...

The principal aim of this paper is to introduce the extended Voigt-type function ${\mathbb{V}}_{\mu ,\nu }(x,y)$ and its counterpart extension ${\mathbb{W}}_{\mu ,\nu }(x,y)$, involving the Neumann function $Y_{\nu }$ in the kernel of the representing integral. The newly defined integra...

Objectives: The objective of this narrative review was to examine the available literature regarding the increasingly popular method of exercise commonly referred to as “Functional Training” and its potential implications on vestibular an...

In this study, the connection between certain subfamilies of harmonic univalent functions is established by utilizing a convolution operator involving the Mittag–Leffler function. The investigation reveals inclusion relations concerning harmoni...

This paper aims to obtain the ${}_{\xi }\mathsf{\Psi }_{\eta }$-extended Whittaker function and its integral representations. This function is defined by using the ${}_{\xi }\mathsf{\Psi }_{\eta }$-confluent hypergeometric function, which was recently extended in terms of the Fox–W...

This paper examines the relationship between the classical polylogarithm function and meromorphic harmonic univalent mappings. Using a convolution operator derived from the polylogarithm function, we define a class of harmonic meromorphic functions a...

In this paper, taking into account the intriguing recent results of Rabotnov functions, Poisson functions, Bessel functions and Wright functions, we consider a new comprehensive subclass ${\mathcal{O}}_{\mu }({\Delta }_1,{\Delta }_2,{\Delta }_3,{\Delta }_4)$ of univalent functio...

In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to f...

This paper shows that certain${ }_3{F}_4$ hypergeometric functions can be expanded in sums of pair products of${ }_2{F}_3$ functions, which reduce in special cases to${ }_2{F}_3$ functions expanded in sums of pair products of${ }_1{F}_2$ functions. This expands...

The normalized analytic function ${\Phi }_N\left(z\right)=1+z-{\displaystyle \frac{z^3}{3}}$, which connects the open unit disk onto a bounded domain within the right half of a nephroid-shaped region, is associated with the bounded turning of functions denoted by $R_n$. It calculates the...

Relying on the Hurwitz formula, we find closed-form formulas for the series over sine and cosine functions through the Hurwitz zeta functions, and using them and another summation formula for trigonometric series, we obtain a finite sum for some seri...

By making use of the concept of basic (or q-) calculus, various families of q-extensions of starlike functions of order $\alpha$ in the open unit disk $\mathbb{U}$ were introduced and studied from many different viewpoints and perspectives. In this p...

In this paper, we consider two functionals of the Fekete–Szegö type ${\mathsf{\Theta }}_f\left(\mu \right)=a_4-\mu a_2{a}_3$ and ${\mathsf{\Phi }}_f\left(\mu \right)=a_2{a}_4-\mu {a_3}^2$ for a real number $\mu$ and fo...

In the theory of special functions, finding correlations between different types of functions is of great interest as unifying results, especially when considering issues such as analytic continuation. In the present paper, the relation between Lambe...

Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbol...

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 Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters a...

Plateaued Boolean functions play an important role in sequence design and cryptography due to their favorable properties such as high nonlinearity, resilience and low additive autocorrelation. In this paper, by modifying the support of certain quadra...

The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass ${\mathcal{A}}_4^{r,s}$ of analytic functions related to the four-leaf domain, to inc...

Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric...

In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Frac...

The Geometric Theory of Analytic Functions was initially developed for the space of functions that are analytic in the unit disk. The convexity and starlikeness of functions are the first geometric ideas considered in this theory. We can notice a sym...

In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the confl...

There has been a considerable evolution of the theory of fractal interpolation function (FIF) over the last three decades. Recently, we introduced a multivariate analogue of a special class of FIFs, which is referred to as $\alpha$-fractal functions, from t...

In numerous geometric and physical applications of complex analysis, estimating the sharp bounds of coefficient-related problems of univalent functions is very important due to the fact that these coefficients describe the core inherent properties of...

Recently, two classes of univalent functions ${\mathcal{S}}_e^{*}$ and ${\mathcal{K}}_e$ were introduced and studied. A function f is in ${\mathcal{S}}_e^{*}$ if it is analytic in the unit disk, $f\left(0\right)=f^{\prime }\left(0\right)-1=0$ and $\frac{z{f}^{\prime }\left(z\right)}{f\left(z\right)}$...

In the present paper, we define and study a new family of holomorphic functions which involve the Bazilevič functions and the $\lambda$-pseudo-starlike functions. We establish coefficient estimates for the first four determinants of the symmetric...

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright functio...

This study examines the necessary requirements for some analytic function subclasses, especially those associated with the generalized Mittag-Leffler function, to be classified as univalent function subclasses that are determined by particular geomet...

A refined asymptotics of the Jacobi theta functions and their logarithmic derivatives have been received. The asymptotics of the Nevanlinna characteristics of the indicated functions and the arbitrary elliptic function have been found. The estimation...

In this paper, we consider the simultaneous approximation of tuples of analytic functions by tuples of shifts of Lerch zeta-functions with arbitrary parameters. We prove that there exists a closed set of tuples of functions analytic in the right-hand...

In this article, we study scalar-on-function regression with functional covariates observed through replicated measurements subject to measurement error. Treating replicated curves as surrogates of an underlying latent process, the proposed framework...

It is difficult to determine whether lung function improves by simple abdominal strengthening exercises, and studies on the correlation of lung function and functional movement are insufficient. Therefore; we aimed to identify the correlation between...

Geometric function theory, a subfield of complex analysis that examines the geometrical characteristics of analytic functions, has seen a sharp increase in research in recent years. In particular, by employing subordination notions, the contributions...

The aim of this paper is the imputation of missing data of COVID-19 hospitalized and intensive care curves in several Spanish regions. Taking into account that the curves of cases, deceases and recovered people are completely observed, a function-on-...

In this article, we establish conditions under which certain entire functions represented as infinite products of their positive zeros are $\alpha$-spirallike of order $cos\left(\alpha \right)/2$. The discussion includes several examples featuring special function...

In this paper, we introduce and investigate a new subclass of bi-univalent Bazilevič-type functions associated with the Gregory generating function. The proposed class is defined by means of subordination and depends on the parameters $\nu$ and $\&$...

A challenging part of studying geometric function theory is figuring out the sharp boundaries for coefficient-related problems that crop up in the Taylor–Maclaurin series of univalent functions. Using Caputo-type fractional derivatives to defin...

We investigate a nonparametric, varying coefficient regression approach for modeling and estimating the regression effects caused by two functionally correlated datasets. Due to modern biomedical technology to measure multiple patient features during...

In this work, we provide a convolution type operator ${\mathsf{\Lambda }}_{\nu ,b}$ that is produced by the generalized Marcum Q-function and examine how it maps to various Janowski-type subclasses of harmonic univalent functions. Since the Marcum Q-function has an...