Definition:Ber Function

Definition

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

The Ber function is defined as:

$\map {\Ber_n} x = \map \Re {\map {J_n} {x \map \exp {\dfrac {3 \pi i} 4} } }$

where:

$\exp$ denotes the exponential function

$x$ is real

$\map \Re z$ denotes the real part of $z$.

Also known as

The Ber function, along with:

its imaginary counterpart the Bei function

the Ker function and Kei function

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

Some sources report and denote the Ber function uncapitalised: ber function.

Also see

• Definition:Bei Function

• Definition:Ker Function
• Definition:Kei Function

• Results about the Ber 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