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,...

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...

{\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...

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

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

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:...

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

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

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

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

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...

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

_{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...

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...

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

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...

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

\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...

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...

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

}}=e^{z}\operatorname {Ein} (z)} where Ein(z) is the entire exponential integral. The exponential integral may also be expressed as Ein ⁡ ( z ) = E 1 ( z ) + γ...

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

calculus, is to perform differential and integral calculus with exponential functions and logarithms. A general exponential function y = ax has a derivative,...

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...