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Date: 21-9-2018
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Date: 21-9-2018
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Date: 21-9-2018
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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).
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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.
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.a
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