scipy.special.exp1#
- scipy.special.exp1(z, out=None) = <ufunc 'exp1'>#
- Exponential integral E1. - For complex \(z \ne 0\) the exponential integral can be defined as [1] \[E_1(z) = \int_z^\infty \frac{e^{-t}}{t} dt,\]- where the path of the integral does not cross the negative real axis or pass through the origin. - Parameters:
- z: array_like
- Real or complex argument. 
- outndarray, optional
- Optional output array for the function results 
 
- Returns:
- scalar or ndarray
- Values of the exponential integral E1 
 
 - Notes - For \(x > 0\) it is related to the exponential integral \(Ei\) (see - expi) via the relation\[E_1(x) = -Ei(-x).\]- References [1]- Digital Library of Mathematical Functions, 6.2.1 https://dlmf.nist.gov/6.2#E1 - Examples - >>> import numpy as np >>> import scipy.special as sc - It has a pole at 0. - >>> sc.exp1(0) inf - It has a branch cut on the negative real axis. - >>> sc.exp1(-1) nan >>> sc.exp1(complex(-1, 0)) (-1.8951178163559368-3.141592653589793j) >>> sc.exp1(complex(-1, -0.0)) (-1.8951178163559368+3.141592653589793j) - It approaches 0 along the positive real axis. - >>> sc.exp1([1, 10, 100, 1000]) array([2.19383934e-01, 4.15696893e-06, 3.68359776e-46, 0.00000000e+00]) - It is related to - expi.- >>> x = np.array([1, 2, 3, 4]) >>> sc.exp1(x) array([0.21938393, 0.04890051, 0.01304838, 0.00377935]) >>> -sc.expi(-x) array([0.21938393, 0.04890051, 0.01304838, 0.00377935])