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Convolutions involving the exponential function and the exponential integral [PDF]

Mathematica Moravica, 2015
The exponential integral ei(λx) and its associated functions ei+(λx) and ei-(λx) are defined as locally summable functions on the real line and their derivatives are found as distributions.
Fisher Brian, Al-Sirehy Fatma
doaj   +3 more sources

Exponential Integral Representations of Theta Functions [PDF]

Computational Methods and Function Theory, 2020
Let $Θ_{3} (z):= \sum_{n\in\mathbb{Z}} \exp (i πn^2 z)$ be the standard Jacobi theta function, which is holomorphic and zero-free in the upper half-plane $\mathbb{H}$, and takes positive values along the positive imaginary axis. We define its logarithm $\logΘ_3(z)$ which is uniquely determined by the requirements that it should be holomorphic in ...
Bakan, Andrew, Hedenmalm, Håkan
openaire   +2 more sources

On the Exponential Integrability of Conjugate Functions [PDF]

Journal of Fourier Analysis and Applications, 2021
AbstractWe relate the exponential integrability of the conjugate function$${\tilde{f}}$$f~to the size of the gap in the essential range off. Our main result complements a related theorem of Zygmund.
H. Gissy, S. Miihkinen, J. A. Virtanen
openaire   +4 more sources

Relation of Some Known Functions in terms of Generalized Meijer G-Functions

Journal of Mathematics, 2021
The aim of this paper is to prove some identities in the form of generalized Meijer G-function. We prove the relation of some known functions such as exponential functions, sine and cosine functions, product of exponential and trigonometric functions ...
Syed Ali Haider Shah, Shahid Mubeen, Gauhar Rahman, Jihad Younis   +3 more
doaj   +1 more source

Fractional-Modified Bessel Function of the First Kind of Integer Order

Mathematics, 2023
The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas.
Andrés Martín, Ernesto Estrada
doaj   +1 more source

Inequalities and pth moment exponential stability of impulsive delayed Hopfield neural networks

Journal of Inequalities and Applications, 2021
In this paper, the pth moment exponential stability for a class of impulsive delayed Hopfield neural networks is investigated. Some concise algebraic criteria are provided by a new method concerned with impulsive integral inequalities.
Yutian Zhang, Guici Chen, Qi Luo
doaj   +1 more source

Fractional Dynamics with Depreciation and Obsolescence: Equations with Prabhakar Fractional Derivatives

Mathematics, 2022
In economics, depreciation functions (operator kernels) are certain decreasing functions, which are assumed to be equal to unity at zero. Usually, an exponential function is used as a depreciation function.
Vasily E. Tarasov
doaj   +1 more source

The heat equation on time scales [PDF]

Opuscula Mathematica, 2023
We present the use of a Fourier transform on time scales to solve a dynamic heat IVP. This is done by inverting a certain exponential function via contour integral. We include some specific examples and directions for further study.
Tom Cuchta, Rui A.C. Ferreira
doaj   +1 more source

Composition Formula for Saigo Fractional Integral Operator Associated with V-Function

Journal of Mathematics, 2022
In this study, we form integral formulas for Saigo’s hypergeometric integral operator involving V-function. Corresponding assertions for the classical Riemann–Liouville (R-L) and Erdélyi–Kober (E-K) fractional integral operator are extrapolated. Also, by
Sunil Chandak, Anita Alaria, Biniyam Shimelis   +2 more
doaj   +1 more source

Some Applications of the Wright Function in Continuum Physics: A Survey

Mathematics, 2021
The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function
Yuriy Povstenko
doaj   +1 more source