Built-in Mathematica Symbol

CosIntegral

CosIntegral[z]
gives the cosine integral function

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

For certain special arguments, CosIntegral 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:

CosIntegral threads element-wise over lists:

Simple exact values are generated automatically:

CosIntegral can be applied to power series:

Find series expansions at infinity:

Average radiated power for a thin linear half-wave antenna:

Plot the imaginary part in the complex plane:

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

Use FullSimplify to simplify expressions containing the cosine integral:

Use FunctionExpand to express CosIntegral through other functions:

Find a numerical root:

Obtain CosIntegral from integrals and sums:

Obtain CosIntegral from a differential equation:

Calculate the Wronskian:

Integrals:

Laplace transform:

CosIntegral can take large values for moderate-size arguments:

A larger setting for $MaxExtraPrecision can be needed:

Nested integrals: