Definition:Bei Function

Definition

Let $J_n$ denote the Bessel function of the first kind.

The Bei function is defined as:

$\map {\Bei_n} x = \map \Im {\map {J_n} {x \map \exp {\dfrac {3 \pi i} 4} } }$

where:

$\exp$ denotes the exponential function

$x$ is real

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

Also known as

The Bei function, along with:

its real counterpart the Ber function

the Ker function and Kei function

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

Some sources report and denote the Bei function uncapitalised: bei function.

Also see

• Definition:Ber Function

• Definition:Ker Function
• Definition:Kei Function

• Results about the Bei function can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Bessel functions
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Bessel functions