Evaluate numerically to high precision:

The precision of the output tracks the precision of the input:

LogIntegral can take complex number inputs:

Evaluate LogIntegral efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix LogIntegral function using MatrixFunction:

Value at the origin:

Singular point of LogIntegral:

Values at infinity:

Find a zero of :

Plot the LogIntegral function:

Plot the real part of :

Plot the imaginary part of :

LogIntegral is defined for all real positive values except 1:

Complex domain:

LogIntegral takes all real values:

LogIntegral is not an analytic function:

Has both singularities and discontinuities:

LogIntegral is neither nondecreasing nor nonincreasing:

LogIntegral is not injective:

LogIntegral is surjective:

LogIntegral is neither non-negative nor non-positive:

LogIntegral is neither convex nor concave:

First derivative:

Higher derivatives:

Indefinite integral of LogIntegral:

Definite integral of LogIntegral:

More integrals:

Taylor expansion for LogIntegral:

Plot the first three approximations for LogIntegral around :

Series expansions on either side of the branch point at :

LogIntegral can be applied to power series:

Primary definition of LogIntegral:

Use FullSimplify to simplify expressions into logarithmic integrals:

Representation through ExpIntegralEi:

Series representation:

TraditionalForm formatting: