Exponential integral Plot of the exponential integral function ⁠ ⁠ for complex ⁠ ⁠ In mathematics, the exponential integral ⁠ ⁠ is a special function on the complex plane. It is defined as one particular …

指数积分的定义 播报 编辑 n阶指数积分 (Exponential Integral)为 对正整数n≥1， 与 之间的递推关系为 当自变量为正实数且 时，函数 满足如下不等式 [1]

The principal value of the exponential integral E 1 ⁡ (z) is defined by ... where the path does not cross the negative real axis or pass through the origin. As in the case of the logarithm (§ 4.2 (i)) there is a …

For x> 0 the integral is understood as a Cauchy principal value. It is extended to the complex plane by analytic continuation of the function on the interval (0, ∞). The complex variant has a branch cut on …

Jan 18, 2026 · The exponential integral function of order n, written as a function of a variable a, is defined as (3.1) E n (a) = ∫ 1 ∞ x n e a x d x I shall restrict myself to cases where n is a non-negative …

The exponential integrals , , , , , , and are defined for all complex values of the parameter and the variable . The function is an analytical functions of and over the whole complex ‐ and ‐planes …

Nov 15, 2022 · The integral identities in this chapter comprise the exponential integral function \ (\mathrm {Ei} (x)=\int _ {-\infty }^x t^ {-1} e^ {-t} dt\), the sine integral Si (x), the cosine integral Ci (x) …

Feb 15, 2026 · 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 …

Feb 9, 2018 · define certain non-elementary (http://planetmath.org/ElementaryFunction) transcendental functions. They are called exponential integrals and denoted usually E 1 and ...

Plot of the exponential integral function E n (z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D It is defined as one particular definite …