Definition:Ber Function
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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
- 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