Riemann-Lebesgue Lemma

The Riemann-Lebesgue Lemma, sometimes also called Mercer's theorem, states that

(1)

for arbitrarily large  and "nice" . Gradshteyn and Ryzhik (2000) state the lemma as follows. If  is integrable on , then

(2)

and

(3)

REFERENCES:

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1101, 2000.