Built-in Mathematica Symbol

SinhIntegral

SinhIntegral[z]
gives the hyperbolic sine integral function

.

For certain special arguments, SinhIntegral automatically evaluates to exact values.

Evaluate numerically:

Evaluate to high precision:

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

SinhIntegral threads element-wise over lists:

SinhIntegral can take complex number inputs:

Simple exact values are generated automatically:

Arguments simplify automatically:

Find series expansions at infinity:

Give the result for an arbitrary symbolic direction

:

SinhIntegral can be applied to power series:

Plot the real part in the complex plane:

Plot the imaginary part in the complex plane:

Use FullSimplify to simplify expressions containing hyperbolic sine integrals:

Find a numerical root:

Obtain SinhIntegral from integrals and sums:

Integrals:

Laplace transform:

SinhIntegral can take large values for moderate-size arguments:

A larger setting for $MaxExtraPrecision can be needed:

In traditional form parentheses are required:

Nested integrals: