## 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 is established using a Contour Integral which satisfies
 (2)

To derive the lemma, write

 (3) (4)

and define the Contour Integral
 (5)

Then
 (6)

Now, if , choose an such that , so
 (7)

But, for ,
 (8)

so
 (9)

As long as , Jordan's lemma
 (10)

then follows.

References

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