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...
20 KB (3,325 words) - 20:06, 11 August 2024
list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals. Indefinite integrals are antiderivative...
12 KB (3,294 words) - 11:10, 19 December 2023
mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions are Si...
18 KB (3,230 words) - 15:34, 12 May 2024
principal value of the function. The function li(x) is related to the exponential integral Ei(x) via the equation li ( x ) = Ei ( ln x ) , {\displaystyle...
6 KB (1,104 words) - 21:51, 7 August 2024
Fubini's theorem (redirect from An elegant rearrangement of a conditionally convergent iterated integral)
the identity to an integral of the complementary Exponential Integral Function: This is how the complementary integral exponential function is defined:...
41 KB (7,843 words) - 02:04, 24 August 2024
{\displaystyle {\frac {e^{-x}}{x}}} (exponential integral) e e x {\displaystyle e^{e^{x}}\,} (in terms of the exponential integral) ln ( ln x ) {\displaystyle...
5 KB (619 words) - 08:30, 27 May 2024
formula Exponential function Exponential generating function Exponential-Golomb coding Exponential growth Exponential hierarchy Exponential integral Exponential...
6 KB (281 words) - 08:56, 22 January 2024
integral in the commutative algebras. In practice the ordered exponential is used in matrix and operator algebras. It is a kind of product integral,...
7 KB (1,232 words) - 01:45, 27 May 2024
Gamma function (redirect from Gamma integral)
Whittaker and Watson, 12.22. "Exponential integral E: Continued fraction representations (Formula 06.34.10.0005)". "Exponential integral E: Continued fraction...
90 KB (13,365 words) - 22:20, 23 August 2024
functions Common integrals in quantum field theory Normal distribution List of integrals of exponential functions Error function Berezin integral Stahl, Saul...
20 KB (4,295 words) - 14:28, 22 July 2024
hyperbolic functions List of integrals of exponential functions List of integrals of logarithmic functions List of integrals of Gaussian functions Gradshteyn...
29 KB (5,617 words) - 21:09, 30 January 2024
Integration by reduction formulae (category Integral calculus)
following integrals contain: Factors of sine Factors of cosine Factors of sine and cosine products and quotients Products/quotients of exponential factors...
17 KB (2,235 words) - 17:13, 26 March 2024
thus easing calculation for numbers greater than μ. Also, since the exponential integral function satisfies the equation l i ( x ) = E i ( ln x ) , {\displaystyle...
1 KB (219 words) - 00:43, 28 April 2024
\operatorname {Ei} } is the exponential integral, E n {\displaystyle \operatorname {E} _{n}} is the generalized exponential integral, erf {\displaystyle \operatorname...
43 KB (7,150 words) - 22:50, 19 August 2024
Logarithmic integral function: Integral of the reciprocal of the logarithm, important in the prime number theorem. Exponential integral Trigonometric integral: Including...
10 KB (1,065 words) - 09:21, 10 August 2024
The exponential function is a mathematical function denoted by f ( x ) = exp ( x ) {\displaystyle f(x)=\exp(x)} or e x {\displaystyle e^{x}} (where...
44 KB (5,755 words) - 12:46, 8 July 2024
correspond to linear combinations of exponentially scaled and time-shifted damped sinusoids in the time domain. Other integral transforms find special applicability...
13 KB (1,278 words) - 16:37, 5 May 2024
{1}{288x^{2}}}-{\frac {139}{51840x^{3}}}-\cdots \ (x\to \infty )} Exponential integral x e x E 1 ( x ) ∼ ∑ n = 0 ∞ ( − 1 ) n n ! x n ( x → ∞ ) {\displaystyle...
12 KB (1,960 words) - 21:23, 15 May 2024
Gamma distribution (category Exponential family distributions)
integral to modeling a range of phenomena due to its flexible shape, which can capture various statistical distributions, including the exponential and...
60 KB (8,717 words) - 19:52, 20 August 2024
_{0}^{\infty }e^{-u}u^{n}\,du} The integral on the left hand side can be expressed in terms of the exponential integral. The integral on the right hand side, after...
17 KB (2,763 words) - 08:12, 22 May 2024
in [W·m−1·K−1] E i ( x ) {\displaystyle \mathrm {Ei} (x)} is the exponential integral, a transcendent mathematical function r {\displaystyle r} is the...
29 KB (3,927 words) - 05:10, 31 July 2024
integrals. A set of rules are applied to the coefficients and exponential terms of the integrand's power series expansion to determine the integral....
68 KB (9,235 words) - 12:25, 23 August 2024
Euler's constant (section Exponential)
entry contains an explicit equation): Expressions involving the exponential integral* The Laplace transform* of the natural logarithm The first term of...
51 KB (7,581 words) - 20:19, 18 August 2024
function Cunningham functions Exponential integral and related functions such as the sine integral, logarithmic integral Hermite polynomials Incomplete...
24 KB (4,566 words) - 19:59, 11 August 2024
following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions...
18 KB (6,282 words) - 10:14, 2 August 2024
ordinary complex exponential. More generally, for complex toruspg 8 X = C n / Λ {\displaystyle X=\mathbb {C} ^{n}/\Lambda } for some integral lattice Λ {\displaystyle...
13 KB (2,207 words) - 21:53, 8 July 2024
In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...
55 KB (10,413 words) - 20:04, 7 June 2024
cut but instead considered as Ei(ρ/n log x) where Ei(x) is the exponential integral. If the trivial zeros are collected and the sum is taken only over...
32 KB (4,247 words) - 22:35, 7 August 2024
and integrals. dom, domain – domain of a function. (Or, more generally, a relation.) End – categories of endomorphisms. Ei – exponential integral function...
20 KB (1,989 words) - 11:23, 31 July 2024
mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function,...
8 KB (1,212 words) - 11:27, 16 August 2023