A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic w...
We derive a new formula for the Hurwitz–Lerch zeta function in terms of the infinite sum of the incomplete gamma function. Special cases are derived in terms of fundamental constants.
The findings of this study are connected with geometric function theory and were acquired using subordination-based techniques in conjunction with the Hurwitz–Lerch Zeta function. We used the Hurwitz–Lerch Zeta function to investigate cer...
Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Funct...
The main aim of this paper is to provide a new generalization of Hurwitz-Lerch Zeta function of two variables. We also investigate several interesting properties such as integral representations, summation formula, and a connection with the generaliz...
The interest in special complex functions and their wide-ranging implementations in geometric function theory (GFT) has developed tremendously. Recently, subordination theory has been instrumentally employed for special functions to explore their geo...
The notion of the fuzzy set was incorporated into geometric function theory in recent years, leading to the emergence of fuzzy differential subordination theory, which is a generalization of the classical differential subordination notion. This artic...
Taking inspiration principally from some of the latest research, we develop a new series representation for the λ-generalized Hurwitz-Lerch zeta functions. This representation led to important new results. The Fourier transform played a founda...
In this article, we establish some new difference equations for the family of λ-generalized Hurwitz–Lerch zeta functions. These difference equations proved worthwhile to study these newly defined functions in terms of simpler functions....
The object of this paper is to derive a double integral in terms of the Hurwitz–Lerch zeta function. Almost all Hurwitz–Lerch zeta functions have an asymmetrical zero-distribution. Special cases are evaluated in terms of fundamental constants. All th...
In the z- domain, differential subordination is a complex technique of geometric function theory based on the idea of differential inequality. It has formulas in terms of the first, second and third derivatives. In this study, we introduce some appli...
We examine the improved infinite sum of the incomplete gamma function for large values of the parameters involved. We also evaluate the infinite sum and equivalent Hurwitz-Lerch zeta function at special values and produce a table of results for easy...
The objective of the present paper is to obtain a quadruple infinite integral. This integral involves the product of the Struve and parabolic cylinder functions and expresses it in terms of the Hurwitz–Lerch Zeta function. Almost all Hurwitz-Le...
We derive a closed-form expression for the infinite sum of the Hurwitz–Lerch zeta function using contour integration. This expression is used to evaluate infinite sum and infinite product formulae involving trigonometric functions expressed in...
The aim of the current document is to evaluate a quadruple integral involving the Chebyshev polynomial of the first kind Tn(x) and derive in terms of the Hurwitz-Lerch zeta function. Special cases are evaluated in terms of fundamental constants. The...
The Ohtsuka–Vălean sum is extended to evaluate an extensive number of trigonometric and hyperbolic sums and products. The sums are taken over finite and infinite domains defined in terms of the Hurwitz–Lerch zeta function, which can...
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...
This article considers a general family of weighted fractional integral operators and utilizes this general operator to establish numerous reverse Minkowski inequalities. When it comes to understanding and investigating convexity and inequality, symm...
In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family SWΣ(δ,γ,λ,s,t,q,r) of normalized holomorphic and bi-univalent functions in the open unit disk U, which are associated with the Bazilevič fun...
Fuzzy differential subordinations, a notion taken from fuzzy set theory and used in complex analysis, are the subject of this paper. In this work, we provide an operator and examine the characteristics of meromorphic functions in the punctured open u...
Often referred to as special functions or mathematical functions, the origin of many members of the remarkably vast family of higher transcendental functions can be traced back to such widespread areas as (for example) mathematical physics, analytic...
In this paper, the authors investigate two special families of series involving the reciprocal central binomial coefficients and Lucas numbers. Connections with several familiar sums representing the integer-valued Riemann zeta function are also poin...
In this paper, we introduce new subclasses RΣ,b,cμ,αλ,δ,τ,Φ and KΣ,b,cμ,αλ,δ,η,Φ of bi-univalent functions in the open unit disk U by using quasi-subordination conditions and determine estimates of the coefficients a2 and a3 for functions of these su...
In this paper, we define Hurwitz–Lerch multi-poly-Cauchy numbers using the multiple polylogarithm factorial function. Furthermore, we establish properties of these types of numbers and obtain two different forms of the explicit formula using St...
This work’s theorems and corollaries present new third-order fuzzy differential subordination and superordination results developed by using a novel convolution linear operator involving the Gaussian hypergeometric function and a previously stu...
In this paper, we investigate a new family of normalized analytic functions and bi-univalent functions associated with the Srivastava–Attiya operator. We use the Faber polynomial expansion to estimate the bounds for the general coefficients |an...
In the fields of science and engineering, tasks involving repeated integrals appear on occasion. The authors’ study on repeated integrals of a class of exponential and logarithmic functions is presented in this publication. The paper includes s...
The article is written with the objectives to introduce a multi-variable hybrid class, namely the Hermite–Apostol-type Frobenius–Euler polynomials, and to characterize their properties via different generating function techniques. Several...
The main purpose of this article is to construct a new class of multivariate Legendre-Hermite-Apostol type Frobenius-Euler polynomials. A number of significant analytical characterizations of these polynomials using various generating function techni...
Boundary behavior of a given important function or its limit values are essential in the whole spectrum of mathematics and science. We consider some tractable cases of limit values in which either a difference of two ingredients or a difference equat...
In this Special Issue, the recent advances in the applications of symmetric functions for mathematics and mathematical physics are reviewed, including many novel techniques in analytic functions, transformation methods, economic growth models, and Hu...
In this part of a series of two papers, we extend the theorems discussed in Part I for infinite series. We then use these theorems to develop distinct novel results involving the Hurwitz zeta function, Riemann zeta function, polylogarithms and Fibona...
A new three-dimensional integral containing f(x,y,z)Iv(xα) is derived where Iv(xα) is the Modified Bessel Function of the first kind and the integral is taken over the infinite cubic space 0<x<∞,0<y<∞,0<z<&in...
We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t13/84+ϵ as t → ∞. For both, the Riem...
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...
The Fourier series expansion of Apostol–tangent polynomials is derived using the Cauchy residue theorem and a complex integral over a contour. This Fourier series and the Hurwitz–Lerch zeta function are utilized to obtain the explicit for...
Chowla’s (inverse) problem (CP) is to mean a proof of linear independence of cotangent-like values from non-vanishing of L(1,χ)=∑n=1∞χ(n)n. On the other hand, we refer to determinant expressions for the (relative) class number...
The transformation formula under the action of a general linear fractional transformation for a generalized Dedekind eta function has been the subject of intensive study since the works of Rademacher, Dieter, Meyer, and Schoenberg et al. However, the...
In this paper, we obtain approximation theorems of classes of analytic functions by shifts L(λ,α,s+iτ) of the Lerch zeta-function for τ∈[T,T+H] where H∈[T27/82,T1/2]. The cases of all parameters, λ,α∈(...
Closed expressions for a number of septuple integrals involving the product of three Bessel functions of the first kind Jα(tβ)Jγ(xδ)Jη(yθ) when the orders α,γ,η are large, are derived in terms of the H...
In this paper, we obtain a new series representation for the generalized Bose–Einstein and Fermi–Dirac functions by using fractional Weyl transform. To achieve this purpose, we obtain an analytic continuation for these functions by genera...
A four-dimensional integral containing g(x,y,z,t)Cn(λ)(x) is derived. Cn(λ)(x) is the Gegenbauer polynomial, g(x,y,z,t) is a product of the generalized logarithm quotient functions and the integral is taken over the region 0≤x≤1,0...
Recently in the paper [Mediterr. J. Math. 2016, 13, 1535–1553], the authors introduced and studied a new operator which was defined as a convolution of the three popular linear operators, namely the Sǎlǎgean operator, the Ruscheweyh operator and...