Results 11 to 20 of about 833,509 (313)
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
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Numerical computation of a generalized exponential integral function [PDF]
Mathematics of Computation, 1974 Series expansions and recurrence relations suitable for numerical computation are developed for the generalized exponential integral functions. Tables of these functions are presented in the microfiche section of this issue.
By W. F. Breig, A. Crosbie
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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
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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
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Concerning some integrals of the generalized exponential-integral function
Computers & Mathematics with Applications, 1992 The main concern of this study consists of generalising expressions applicable to the exponential integral of positive integer order to that of general real order. Associated moments connected with simple powers of the variable of integration are discussed along with the so-called polynomial moments in which such standard polynomials as that of ...
C. Chiccoli, S. Lorenzutta, G. Maino
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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
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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
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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 +2 more
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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
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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
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