Modified Bessel Differential Equation
المؤلف:
Abramowitz, M. and Stegun, I. A
المصدر:
in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.
الجزء والصفحة:
...
23-6-2018
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Modified Bessel Differential Equation
The second-order ordinary differential equation
 |
(1)
|
The solutions are the modified Bessel functions of the first and second kinds, and can be written
where 
is a Bessel function of the first kind, 
is a Bessel function of the second kind, 
is a modified Bessel function of the first kind, and 
is modified Bessel function of the second kind.
If 
, the modified Bessel differential equation becomes
 |
(4)
|
which can also be written
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). §9.6.1 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.
Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 121, 1997.
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