Definition:Kei Function

Definition

Let $K_n$ denote the modified Bessel function of the second kind.

The Kei function is defined as:

$\map {\Kei_n} x = \map \Im {\map {K_n} {x \map \exp {\dfrac {\pi i} 4} } }$

where:

$\exp$ denotes the exponential function

$x$ is real

$\map \Im z$ denotes the imaginary part of $z$.

Also known as

The Kei kunction, along with:

its real counterpart the Ker function

the Ber function and Bei function

are known collectively as the Kelvin functions, for Lord Kelvin.

Some sources report and denote the Kei function uncapitalised: kei function.

Also see

• Definition:Ker Function

• Definition:Ber Function
• Definition:Bei Function

• Results about the Kei function can be found here.

Sources

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