“Jordan's Lemma”的概念、定义、习题解题方法及翻译-数学辞典

单词

Jordan's Lemma

释义

Jordan's Lemma

Jordan's lemma shows the value of the Integral

(1)

along the Real Axis is 0 for ``nice'' functions which satisfy

. This isestablished using a Contour Integral

which satisfies

(2)

To derive the lemma, write

			(3)
			(4)

and define the Contour Integral

(5)

Then

Now, if

, choose an

such that

, so

(7)

But, for

(8)


			(9)

As long as

, Jordan's lemma

(10)

then follows.

See also Contour Integration

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 406-408, 1985.

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