# jax.scipy.special.expi¶

jax.scipy.special.expi = <jax._src.custom_derivatives.custom_jvp object>[source]

Exponential integral Ei.

LAX-backend implementation of expi().

Original docstring below.

For real $$x$$, the exponential integral is defined as 1

$Ei(x) = \int_{-\infty}^x \frac{e^t}{t} dt.$

For $$x > 0$$ the integral is understood as a Cauchy principle value.

It is extended to the complex plane by analytic continuation of the function on the interval $$(0, \infty)$$. The complex variant has a branch cut on the negative real axis.

Parameters
• x (array_like) – Real or complex valued argument

• out (ndarray, optional) – Optional output array for the function results

Returns

Values of the exponential integral

Return type

scalar or ndarray

References

1

Digital Library of Mathematical Functions, 6.2.5 https://dlmf.nist.gov/6.2#E5