The symbol ker 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 ker_nu(z) function is defined as the real part of


where K_nu(z) is a modified Bessel function of the second kind. Therefore


where R[z] is the real part.

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

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



The special case nu=0 is commonly denoted ker_0(z)=ker(z) and has the plot shown above. ker(z) has the series expansion


where psi(z) 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

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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 ber_nu(x), beinu(x), ker_nu(x) and kei_nu(x)." §1.7 in Integrals and Series, Vol. 3: More Special Functions. Newark, NJ: Gordon and Breach, pp. 29-30, 1990.

Referenced on Wolfram|Alpha


Cite this as:

Barile, Margherita and Weisstein, Eric W. "Ker." From MathWorld--A Wolfram Web Resource.

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