“Lommel Function”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lommel Function

释义

Lommel Function

There are several functions called ``Lommel functions.'' One type of Lommel function is the solution to the LommelDifferential Equation with a Plus Sign,

(1)

where

(2)

Here,

and

are Bessel Functions of the First andSecond Kinds (Watson 1966, p. 346). If a minus sign precedes

, then thesolution is

(3)

where

and

are Modified Bessel Functions of the First and Second Kinds.

Lommel functions of two variables are related to the Bessel Function of the First Kind and arise in the theory ofdiffraction and, in particular, Mie scattering (Watson 1966, p. 537),

			(4)
			(5)

See also Lommel Differential Equation, Lommel Polynomial

References

Chandrasekhar, S. Radiative Transfer. New York: Dover, p. 369, 1960.

Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, 1966.

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