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Built-in Mathematica Symbol

KelvinKei

KelvinKei[z]
gives the Kelvin function

KelvinKei[n, z]
gives the Kelvin function

For positive real values of parameters, . For other values, is defined by analytic continuation.

KelvinKei[n, z] has a branch cut discontinuity in the complex z plane running from to .

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

Evaluate numerically:

Plot

Series at the origin:

Evaluate numerically:

Plot

Series at the origin:

Evaluate for complex arguments and orders:

Evaluate to high precision:

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

KelvinKei can be applied to a power series:

Solve the Kelvin differential equation:

Plot the radial density profile for AC current in a hollow cylinder:

Use FullSimplify to simplify expressions involving Kelvin functions:

Use FunctionExpand to expand Kelvin functions of half-integer orders:

Integrate expressions involving Kelvin functions: