lommel Differential Equation
المؤلف:
Chandrasekhar, S
المصدر:
Radiative Transfer. New York: Dover
الجزء والصفحة:
...
22-6-2018
1921
lommel Differential Equation
The Lommel differential equation is a generalization of the Bessel differential equation given by
 |
(1)
|
or, in the most general form, by
 |
(2)
|
The case 
is the most common (Watson 1966, p. 345; Zwillinger 1997, p. 125; Gradshteyn and Ryzhik 2000, p. 937), and its solutions are given by
where 
are Lommel functions. Note that 
is most commonly written simply as 
.
The second-order ordinary differential equation
 |
(5)
|
is sometimes also called the Lommel differential equation
REFERENCES:
Chandrasekhar, S. Radiative Transfer. New York: Dover, p. 369, 1960.
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, 2000.
Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.
Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 125, 1997
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