The Riemann-Lebesgue Lemma, sometimes also called Mercer's theorem, states that
(1)
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for arbitrarily large and "nice" . Gradshteyn and Ryzhik (2000) state the lemma as follows. If is integrable on , then
(2)
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and
(3)
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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)
|
Weisstein, Eric W. "Riemann-Lebesgue Lemma." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Riemann-LebesgueLemma.html