Related papers: On a generalized three-parameter Wright function o…
In this paper we study asymptotic properties of families of zeta and $L$-functions over finite fields. We do it in the context of three main problems: the basic inequality, the Brauer--Siegel type results and the results on distribution of…
We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of locally convex Hausdorff spaces can be extended to a Fourier…
In this note, we extend Euler's transformation formula from the alternating series to more general series. Then we give new expressions for the Riemann zeta function $\zeta(s)$ by the generalized difference operator $\Delta_{c}$, which…
In the present paper we introduce some expansions, based on the falling factorials, for the Euler Gamma function and the Riemann Zeta function. In the proofs we use the Fa\'a di Bruno formula, Bell polynomials, potential polynomials,…
Due to their flexibility, Fox-$H$ functions are widely studied and applied to many research topics, such as astrophysics, mechanical statistic, probability, etc. Well-known special cases of Fox-$H$ functions, such as Mittag-Leffler and…
In this paper we study the almost everywhere convergence of the expansions related to the self-adjoint extension of the Laplace-Beltrami operator on the unit sphere. The sufficient conditions for summability is obtained. The more general…
In this article, we explore a natural extension of the quadratic parametrization introduced in our previous work. By replacing the integer $n$ by $n^s$ ($ s\in\mathbb{R}, s>1$) and allowing the parameters to be real, we obtain for each…
The difficulties arising in the investigation of finite-size scaling in $d$--dimensional O(n) systems with strong anisotropy and/or long-range interaction, decaying with the interparticle distance $r$ as $r^{-d-\sigma}$ ($0<\sigma\leq2$),…
The main focus of the present paper is to investigate several generating functions for a certain classes of functions associated to the Fox-Wright functions. In particular, certain generating functions for a class of function involving the…
The main aim of this paper is to describe the most adequate generalization of the Cauchy-Riemann system fixing properties of classical functions in octonionic case. An octonionic generalization of the Laplace transform is introduced.…
The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit…
We derive the asymptotic expansion (asymptotics with an arbitrary number of error terms) of k-regular graphs by applying the Laplace method on a recent exact formula from Caizergues and de Panafieu (2023). We also deduce the asymptotic…
The two-parametric Mittag-Leffler function (MLF), $E_{\alpha,\beta}$, is fundamental to the study and simulation of fractional differential and integral equations. However, these functions are computationally expensive and their numerical…
The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…
In this paper, we construct a family of generalized $L$-functions, one for each point $z$ in the upper half-plane. We prove that as $z$ approaches $i\infty$, these generalized $L$-functions converge to an $L$-function which can be written…
In this thesis we show that the partial sums of the Maclaurin series for a certain class of entire functions possess scaling limits in various directions in the complex plane. In doing so we obtain information about the zeros of the partial…
We obtain the asymptotic expansion for the Gauss hypergeometric function \[F(a-\lambda,b+\lambda;c+i\alpha\lambda;z)\] for $\lambda\rightarrow+\infty$ with $a$, $b$ and $c$ finite parameters by application of the method of steepest…
In [90] the first-named author gave a working definition of a family of automorphic L-functions. Since then there have been a number of works [33], [107], [67] [47], [66] and especially [98] by the second and third-named authors which make…
A method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transform of the given asymptotic series, with the…
In this paper, we prove the strict monotonicity in the parameter $\rho$ of the Mittag-Leffler functions $E_\rho(-t^\rho)$ and $t^{\rho -1}E_{\rho,\rho}(-t^\rho)$. Then, these results are applied to solve the inverse problem of determining…