Evaluate numerically to high precision:

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

SinhIntegral can take complex number inputs:

Evaluate SinhIntegral efficiently at high precision:

SinhIntegral threads elementwise over lists:

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 SinhIntegral function using MatrixFunction:

Value at the origin:

Values at infinity:

Find the real root of the equation :

Plot the SinhIntegral function:

Plot the real part of :

Plot the imaginary part of :

SinhIntegral is defined for all real and complex values:

SinhIntegral takes all the real values:

SinhIntegral is an odd function:

SinhIntegral is an analytic function of x:

SinhIntegral is non-decreasing:

SinhIntegral is injective:

SinhIntegral is surjective:

SinhIntegral is neither non-negative nor non-positive:

SinhIntegral has no singularities or discontinuities:

SinhIntegral is neither convex nor concave:

First derivative:

Higher derivatives:

Formula for the derivative:

Indefinite integral of SinhIntegral:

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

More integrals:

Taylor expansion for SinhIntegral:

Plot the first three approximations for SinhIntegral around :

General term in the series expansion of SinhIntegral:

Find series expansions at infinity:

Give the result for an arbitrary symbolic direction :

SinhIntegral can be applied to power series:

Compute the Laplace transform using LaplaceTransform:

HankelTransform:

Primary definition of SinhIntegral:

Argument simplifications:

Simplify expressions to SinhIntegral:

Representation in terms of SinIntegral:

Series representation of SinhIntegral:

SinhIntegral can be represented in terms of MeijerG:

SinhIntegral can be represented as a DifferentialRoot:

TraditionalForm formatting: