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...

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

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

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:...

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

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

in integral evaluations and as a value of special functions. It is named after Benjamin Gompertz. It can be defined via the exponential integral as:...

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

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

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

_{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...

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

and the exponential period integral of γ {\displaystyle \gamma } one obtains all positive rational digamma values as a sum of two exponential period integrals...

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

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...

the exponential function is the unique real function which maps zero to one and has a derivative everywhere equal to its value. The exponential of a...

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

\mathrm {d} t,} the integral can be evaluated explicitly. To do this, it is convenient to start without the factor i in the exponential, so that large deviations...

The exponential integral En (x)" (1974, with Ruth Zucker) "Automatic computing methods for special functions. Part III. The sine, cosine, exponential integrals...

Liouvillian functions, including the exponential integral (Ei), logarithmic integral (Li or li) and Fresnel integrals (S and C). the error function, e r...

mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear...

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

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

often not clear whether the stretched exponential function should be used to describe the differential or the integral distribution function—or neither. In...

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

{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...

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

ordinary complex exponential. More generally, for complex torus: 8  X = C n / Λ {\displaystyle X=\mathbb {C} ^{n}/\Lambda } for some integral lattice Λ {\displaystyle...