The beta integral method proved itself as a simple but nonetheless powerful method for generating hypergeometric identities at a fixed argument. In this paper, we propose a generalization by substituting the beta density with a particular type of Mei...
In this paper we consider some integral representations for the evaluation of the coefficients of the Taylor series for the Riemann zeta function about a point in the complex half-plane
On the one hand, convex functions are important to derive rigorous convergence rates, and on the other, synchronous functions are significant to solve statistical problems using Chebyshev inequalities. Therefore, fractional integral inequalities invo...
In this paper, motivated by the contributions of several researchers, including (for example) Riemann, Kronecker, Lerch, Ramanujan, and Glaisher on some special integrals known as Mordell’s integrals, we consider the problem of the evaluation o...
Using Mellin-Barnes contour integrals, we aim at suggesting a q-analogue (q-extension) of the several variable Aleph-function. Then we present Riemann Liouville fractional q-integral and q-differential formulae for the q-extended several variable Ale...
In this study, a novel and exact closed-form expression for detection probability of energy detection (ED) in terms of Meijer’s G-function over α-μ generalized fading channels was derived. It is more accurate and practical than the exi...
We extend the classical Euler-type integral representations for the Appell functions
A non-homogeneous fractional differential equation with a variable coefficient involving a Caputo fractional derivative is considered. The equation is first transformed into an integral equation and then solved using the method of successive approxim...
Compared with a monostatic radar, airborne distributed coherent radar (ADCR) has been widely applied thanks to its flexibility, greater degree of freedom, stronger detection, and anti-jamming ability. Unlike distributed ground-based radar, the precon...
We extend previous research to derive three additional M-1-dimensional integral representations over the interval
This is a brief exposition of some statistical techniques utilized to obtain several useful integral equations involving G-functions.
This research is inspired from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean vector and unknown covariance matrix. The focus is...
Addition theorems have been indispensable tools for the reduction of quantum transition amplitudes. They are normally utilized at the start of the process to move the angular dependence within plane waves, Coulomb potentials, and the like, into a sum...
This study investigates the performance of a mixed dual-hop free-space optical/underwater wireless optical communication (FSO-UWOC) system employing a decode-and-forward (DF) relay protocol, particularly under a comprehensive hybrid channel fading mo...
Free-space optical (FSO) communication offers high-capacity wireless connectivity but is highly susceptible to atmospheric impairments in arid and dust-prone environments. This paper presents a closed-form outage analysis for FSO links subject to Bet...
Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three largely distinct velocity distributions, namely...
We apply the recently proposed analytic extension of formal indicial umbral calculus to the evaluation and structural interpretation of Bessel moments, replacing formal symbolic constructions with Mellin–Barnes analytic transmutations. The clas...
We apply known special functions from the literature (and these include the Fox
In this paper, the secrecy performance of a mixed free space optical (FSO)/radio frequency (RF) integrated satellite-high altitude platform (HAP) relaying networks for terrestrial multiusers with the existence of an eavesdropper is investigated. In t...
In the survey Kiryakova: “A Guide to Special Functions in Fractional Calculus” (published in this same journal in 2021) we proposed an overview of this huge class of special functions, including the Fox H-functions, the Fox–Wright g...
The Low Earth Orbit (LEO) small satellites are extensively used for global connectivity to enable services in underpopulated, remote or underdeveloped areas. Their inherent broadcast nature exposes LEO–terrestrial communication links to severe...
This work analyzes the ergodic capacity behavior of reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) systems with a finite and arbitrary number of antennas and RIS elements under Nakagami-m fading conditions. By...
Dedicated to the memory of Professor Richard Askey (1933–2019) and to pay tribute to the Bateman Project. Harry Bateman planned his “shoe-boxes” project (accomplished after his death as Higher Transcendental Functions, Vols. 1–3, 1953–1955, under the...
The Riemann-Liuoville fractional integrals are the simplest and most popular operators of the classical fractional calculus. But their variants, the Erdélyi-Kober operators of fractional integration, have many more applications due to the free...
In this paper, we analyze the confidentiality of a hybrid radio frequency (RF)/free-space optical (FSO) system with regard to physical layer security (PLS). In this system, signals are transmitted between the source and destination using RF and FSO l...
To improve the performance of fee-space optical communication systems, this paper analyzes the performance of a relay-aided hybrid fee-space optical (FSO)/radio frequency (RF) cooperation system based on a selective combination and decoding forward t...
This paper proposes a generalized space time block coded (GSTBC) enhanced fully optical generalized spatial modulation (EFOGSM) system based on Málaga (M) turbulent channel. GSTBC-EFOGSM adopts the hybrid concept of generalized space time bloc...
Evaluation of images of special functions under operators of fractional calculus has become a hot topic with hundreds of recently published papers. These are growing daily and we are able to comment here only on a few of them, including also some of...