Show that S 0 -Rsin iR cos de → 0 as R→∞0. e e

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Show that
π
S
-R sin iRcos do → O
e
(Hint: Split the integral as f
Ső
S.
= f + f¯ + ſ. Note that the first and
third integrals can controlled in terms of € because le-RsineiR cos | ≤ 1
for the range of 0 we consider, while for the second term we have
-R sin iR cos≤é
le-
whenever € [E, TT - €].)
as R→ ∞.
-R sin €
9
Transcribed Image Text:Show that π S -R sin iRcos do → O e (Hint: Split the integral as f Ső S. = f + f¯ + ſ. Note that the first and third integrals can controlled in terms of € because le-RsineiR cos | ≤ 1 for the range of 0 we consider, while for the second term we have -R sin iR cos≤é le- whenever € [E, TT - €].) as R→ ∞. -R sin € 9
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