has at least two different meanings
in mathematics. It can refer to a special function related to Bessel functions, or
(written either with a capital or lower-case "K"), it can denote a kernel.
function is defined as the real part of
is a modified
Bessel function of the second kind. Therefore
is the real
It is implemented in the
Wolfram Language as [ KelvinKer nu,
has a complicated series given
by Abramowitz and Stegun (1972, p. 379).
The special case
is commonly denoted
and has the plot shown above.
has the series expansion
is the digamma
function (Abramowitz and Stegun 1972, p. 380).
"ker" is also an abbreviation for "
kernel" of a group homomorphism.
See also Bei
Portions of this entry contributed by
Barile Explore with Wolfram|Alpha
References Abramowitz, M. and Stegun, I. A. (Eds.). "Kelvin Functions." §9.9 in
New York: Dover, pp. 379-381, 1972. Handbook
of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. Prudnikov, A. P.; Marichev,
O. I.; and Brychkov, Yu. A. "The Kelvin Functions , ,
and ." §1.7 in Newark, NJ: Gordon and Breach,
pp. 29-30, 1990. Integrals
and Series, Vol. 3: More Special Functions. Referenced on Wolfram|Alpha Ker
Cite this as:
Barile, Margherita and Weisstein, Eric W. "Ker." From --A Wolfram Web
Resource. MathWorld https://mathworld.wolfram.com/Ker.html