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Date: 19-7-2019
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Date: 18-8-2019
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Date: 22-5-2019
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Kelvin defined the Kelvin functions bei and ber according to
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(1) |
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(2) |
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(3) |
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(4) |
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
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(5) |
where is a modified Bessel function of the second kind. For the special case
,
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(6) |
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(7) |
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.
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