The symbol 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 .

The function is defined as the real part of

(1)

where is a modified
Bessel function of the second kind . Therefore

(2)

where is the real
part .

It is implemented in the Wolfram Language as KelvinKer [nu ,
z ].

has a complicated series given
by Abramowitz and Stegun (1972, p. 379).

850

The special case
is commonly denoted
and has the plot shown above.
has the series expansion

(3)

where is the digamma
function (Abramowitz and Stegun 1972, p. 380).

"ker" is also an abbreviation for "group
kernel " of a group homomorphism.

See also Bei ,

Ber ,

Group
Kernel ,

Kei ,

Kelvin Functions
Portions of this entry contributed by Margherita
Barile

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. Referenced on Wolfram|Alpha Ker
Cite this as:
Barile, Margherita and Weisstein, Eric W. "Ker." From MathWorld --A Wolfram Web
Resource. https://mathworld.wolfram.com/Ker.html

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