scipy.special.expn#
- scipy.special.expn(n, x, out=None) = <ufunc 'expn'>#
- Generalized exponential integral En. - For integer \(n \geq 0\) and real \(x \geq 0\) the generalized exponential integral is defined as [dlmf] \[E_n(x) = x^{n - 1} \int_x^\infty \frac{e^{-t}}{t^n} dt.\]- Parameters:
- narray_like
- Non-negative integers 
- xarray_like
- Real argument 
- outndarray, optional
- Optional output array for the function results 
 
- Returns:
- scalar or ndarray
- Values of the generalized exponential integral 
 
 - References [dlmf]- Digital Library of Mathematical Functions, 8.19.2 https://dlmf.nist.gov/8.19#E2 - Examples - >>> import numpy as np >>> import scipy.special as sc - Its domain is nonnegative n and x. - >>> sc.expn(-1, 1.0), sc.expn(1, -1.0) (nan, nan) - It has a pole at - x = 0for- n = 1, 2; for larger- nit is equal to- 1 / (n - 1).- >>> sc.expn([0, 1, 2, 3, 4], 0) array([ inf, inf, 1. , 0.5 , 0.33333333]) - For n equal to 0 it reduces to - exp(-x) / x.- >>> x = np.array([1, 2, 3, 4]) >>> sc.expn(0, x) array([0.36787944, 0.06766764, 0.01659569, 0.00457891]) >>> np.exp(-x) / x array([0.36787944, 0.06766764, 0.01659569, 0.00457891]) - For n equal to 1 it reduces to - exp1.- >>> sc.expn(1, x) array([0.21938393, 0.04890051, 0.01304838, 0.00377935]) >>> sc.exp1(x) array([0.21938393, 0.04890051, 0.01304838, 0.00377935])