Built-in Mathematica Symbol

CoshIntegral

CoshIntegral[z]
gives the hyperbolic cosine integral

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CoshIntegral[z] has a branch cut discontinuity in the complex z plane running from - to 0.

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

Evaluate numerically:

Evaluate for complex arguments:

Evaluate to high precision:

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

CoshIntegral threads element-wise over lists:

Simple exact values are generated automatically:

CoshIntegral can be applied to power series:

Find asymptotic series expansion at infinity:

Plot the imaginary part in the complex plane:

Use FullSimplify to simplify expressions containing the hyperbolic cosine integral:

Use FunctionExpand to express CoshIntegral through other functions:

Find a numerical root:

Obtain CoshIntegral from integrals and sums:

Integrals:

CoshIntegral can take large values for moderate-size arguments:

A larger setting for $MaxExtraPrecision can be needed:

Nested integrals:

Plot the logarithm of the absolute value in the complex plane: