Kelvin Differential Equation
المؤلف:
Abramowitz, M. and Stegun, I. A
المصدر:
"Kelvin Functions." §9.9 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
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13-6-2018
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Kelvin Differential Equation
The complex second-order ordinary differential equation
 |
(1)
|
(Abramowitz and Stegun 1972, p. 379; Zwillinger 1997, p. 123), whose solutions can be given in terms of the Kelvin functions as
(Abramowitz and Stegun 1972, p. 379).
The general solution is
 |
(6)
|
where 
is a Bessel function of the first kind and 
is a Bessel function of the second kind.
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.
Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 123, 1997.
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