spycial.ei

spycial.ei = <numba._DUFunc 'ei'>

Exponential integral \(Ei(x)\).

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.

Parameters:

• x (array-like) – Points on the real line
• out (ndarray, optional) – Output array for the values of ei at x

Returns:

Values of ei at x

Return type:

ndarray

Notes

The exponential integrals \(E_1\) and \(Ei\) satisfy the relation

\[E_1(x) = -Ei(-x)\]

for \(x > 0\).

See also

e1

Exponential integral \(E_1\)

References

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