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In mathematics, the exponential integral Ei is a special function on the complex plane. It is defined as one particular definite integral of the ratio between an exponential function and its argument .
Toyesh Prakash Sharma, Etisha Sharma, "Putting Forward Another Generalization Of The Class Of Exponential Integrals And Their Applications.," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.10, Issue.2, pp.1-8, 2023.
A. Dieckmann, Table of Integrals (Elliptic Functions, Square Roots, Inverse Tangents and More Exotic Functions): Indefinite Integrals Definite Integrals; Math Major: A Table of Integrals; O'Brien, Francis J. Jr. "500 Integrals of Elementary and Special Functions". Derived integrals of exponential, logarithmic functions and special functions.
The angular integration of an exponential in cylindrical coordinates can be written in terms of Bessel functions of the first kind [4] [5]: 113 ( ()) = and ( ()) = (). For applications of these integrals see Magnetic interaction between current loops in a simple plasma or electron gas .
Exponential integrators are a class of numerical methods for the solution of ordinary differential equations, specifically initial value problems. This large class of methods from numerical analysis is based on the exact integration of the linear part of the initial value problem.
In mathematics, the exponential function can be characterized in many ways. This article presents some common characterizations, discusses why each makes sense, and proves that they are all equivalent. The exponential function occurs naturally in many branches of mathematics. Walter Rudin called it "the most important function in mathematics". [1]
The financial sector was up over 30% in 2024 and is poised for another strong year in 2025, according to a report from Fidelity. Even though the financial sector fluctuates based on the economy ...
and it is classified as one of the generalized exponential integral functions. All of the functions Ki n ( x ) {\displaystyle \operatorname {Ki} _{n}(x)} for positive integer n are monotonously decreasing functions, because e − x {\displaystyle e^{-x}} is a decreasing function and sin x {\displaystyle \sin x} is a positive increasing ...