Evaluate numerically to high precision:

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

Evaluate for complex arguments:

Evaluate SinIntegral 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 SinIntegral function using MatrixFunction:

Value at a fixed point:

Values at infinity:

Find a local maximum as a root of :

Plot the SinIntegral function:

Plot the real part of :

Plot the imaginary part of :

SinIntegral is defined for all real and complex values:

Approximate function range of SinIntegral:

SinIntegral is an odd function:

SinIntegral is an analytic function of x:

SinIntegral is neither non-decreasing nor non-increasing:

SinIntegral is not injective:

SinIntegral is not surjective:

SinIntegral is neither non-negative nor non-positive:

SinIntegral has no singularities or discontinuities:

SinIntegral is neither convex nor concave:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of SinIntegral:

Definite integral of an odd integrand over an interval centered at the origin is 0:

More integrals:

Taylor expansion for SinIntegral:

Plot the first three approximations for SinIntegral around :

General term in the series expansion of SinIntegral:

Find series expansion at infinity:

Give the result for an arbitrary symbolic direction :

SinIntegral can be applied to power series:

Use FullSimplify to simplify expressions containing sine integrals:

Simplify expressions to SinIntegral:

Argument simplifications:

Series representation of SinIntegral:

SinIntegral can be represented in terms of MeijerG:

SinIntegral can be represented as a DifferentialRoot:

TraditionalForm formatting: