The function is defined through the equation
|
(1)
|
where is a Bessel
function of the first kind, so
|
(2)
|
where is the real
part.
The function is implemented in the Wolfram Language as KelvinBer[nu,
z].
The function has the series expansion
|
(3)
|
where is the gamma
function (Abramowitz and Stegun 1972, p. 379), which can be written in closed
form as
|
(4)
|
where is a modified
Bessel function of the first kind.
The special case ,
commonly denoted ,
corresponds to
|
(5)
|
where is the zeroth order Bessel
function of the first kind. The function has the series expansion
|
(6)
|
which can be written in closed form as
See also
Bei,
Bessel Function,
Kei,
Kelvin
Functions,
Ker
Explore with Wolfram|Alpha
References
Abramowitz, M. and Stegun, I. A. (Eds.). "Kelvin Functions." §9.9 in Handbook
of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, pp. 379-381, 1972.Prudnikov, A. P.; Marichev,
O. I.; and Brychkov, Yu. A. "The Kelvin Functions , ,
and ." §1.7 in Integrals
and Series, Vol. 3: More Special Functions. Newark, NJ: Gordon and Breach,
pp. 29-30, 1990.Spanier, J. and Oldham, K. B. "The Kelvin
Functions." Ch. 55 in An
Atlas of Functions. Washington, DC: Hemisphere, pp. 543-554, 1987.Referenced
on Wolfram|Alpha
Ber
Cite this as:
Weisstein, Eric W. "Ber." From MathWorld--A
Wolfram Web Resource. https://mathworld.wolfram.com/Ber.html
Subject classifications