Kelvin defined the Kelvin functions bei and ber
according to
where
is a Bessel function of the first kind
and
is a modified Bessel function
of the first kind. These functions satisfy the Kelvin
differential equation.
Similarly, the functions kei and ker
by
|
(5)
|
where
is a modified Bessel function
of the second kind. For the special case ,
See also
Bei,
Ber,
Kei,
Kelvin Differential Equation,
Ker
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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
Kelvin Functions
Cite this as:
Weisstein, Eric W. "Kelvin Functions."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KelvinFunctions.html
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