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...

list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals. Indefinite integrals are antiderivative...

mathematics, trigonometric integrals are a family of nonelementary integrals involving trigonometric functions. The different sine integral definitions are Si...

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...

the identity to an integral of the complementary Exponential Integral Function: This is how the complementary integral exponential function is defined:...

{\displaystyle {\frac {e^{-x}}{x}}} (exponential integral) e e x {\displaystyle e^{e^{x}}\,} (in terms of the exponential integral) ln ⁡ ( ln ⁡ x ) {\displaystyle...

formula Exponential function Exponential generating function Exponential-Golomb coding Exponential growth Exponential hierarchy Exponential integral Exponential...

integral in the commutative algebras. In practice the ordered exponential is used in matrix and operator algebras. It is a kind of product integral,...

Whittaker and Watson, 12.22. "Exponential integral E: Continued fraction representations (Formula 06.34.10.0005)". "Exponential integral E: Continued fraction...

functions Common integrals in quantum field theory Normal distribution List of integrals of exponential functions Error function Berezin integral Stahl, Saul...

hyperbolic functions List of integrals of exponential functions List of integrals of logarithmic functions List of integrals of Gaussian functions Gradshteyn...

following integrals contain: Factors of sine Factors of cosine Factors of sine and cosine products and quotients Products/quotients of exponential factors...

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...

\operatorname {Ei} } is the exponential integral, E n {\displaystyle \operatorname {E} _{n}} is the generalized exponential integral, erf {\displaystyle \operatorname...

Logarithmic integral function: Integral of the reciprocal of the logarithm, important in the prime number theorem. Exponential integral Trigonometric integral: Including...

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...

correspond to linear combinations of exponentially scaled and time-shifted damped sinusoids in the time domain. Other integral transforms find special applicability...

{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...

integral to modeling a range of phenomena due to its flexible shape, which can capture various statistical distributions, including the exponential and...

_{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...

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...

integrals. A set of rules are applied to the coefficients and exponential terms of the integrand's power series expansion to determine the integral....

entry contains an explicit equation): Expressions involving the exponential integral* The Laplace transform* of the natural logarithm The first term of...

function Cunningham functions Exponential integral and related functions such as the sine integral, logarithmic integral Hermite polynomials Incomplete...

following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions...

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...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

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...

and integrals. dom, domain – domain of a function. (Or, more generally, a relation.) End – categories of endomorphisms. Ei – exponential integral function...

mathematics, an exponential sum may be a finite Fourier series (i.e. a trigonometric polynomial), or other finite sum formed using the exponential function,...