1.- Use Laplace's method to obtain an asymtpotic expansion valid for x → ∞ of the complementary error function erfc(x) = 2/17√ √ p°³° ՐՁ e -t2 dt = 2 -x2 e S -2tx-t2 e e dt, (Note the Compare the asymp- totic results with the exact values erfc(2) = 0.004677735... and erfc(4) = 0.00000 00154 173.... Is the asymptotic expansion convergent? [Hints: Note that the function -2t (which is part of the exponent in the exponential e in the second integral above) has its maximum at an endpoint of the integration interval. Expand exp (-2) in a power series around the origin.] -2tx
1.- Use Laplace's method to obtain an asymtpotic expansion valid for x → ∞ of the complementary error function erfc(x) = 2/17√ √ p°³° ՐՁ e -t2 dt = 2 -x2 e S -2tx-t2 e e dt, (Note the Compare the asymp- totic results with the exact values erfc(2) = 0.004677735... and erfc(4) = 0.00000 00154 173.... Is the asymptotic expansion convergent? [Hints: Note that the function -2t (which is part of the exponent in the exponential e in the second integral above) has its maximum at an endpoint of the integration interval. Expand exp (-2) in a power series around the origin.] -2tx
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 51PS
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![1.- Use Laplace's method to obtain an asymtpotic expansion valid for x → ∞ of the complementary
error function
erfc(x) = 2/17√ √ p°³°
ՐՁ
e
-t2
dt =
2
-x2
e
S
-2tx-t2
e
e
dt,
(Note the
Compare the asymp-
totic results with the exact values erfc(2) = 0.004677735... and erfc(4) = 0.00000 00154 173.... Is
the asymptotic expansion convergent? [Hints: Note that the function -2t (which is part of the
exponent in the exponential e in the second integral above) has its maximum at an endpoint
of the integration interval. Expand exp (-2) in a power series around the origin.]
-2tx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fafade1a9-1f29-4d84-b55a-a57e5a303c8b%2F8fd4b6f0-e22f-472e-b373-16fc877c3607%2Fmn9t5ed_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.- Use Laplace's method to obtain an asymtpotic expansion valid for x → ∞ of the complementary
error function
erfc(x) = 2/17√ √ p°³°
ՐՁ
e
-t2
dt =
2
-x2
e
S
-2tx-t2
e
e
dt,
(Note the
Compare the asymp-
totic results with the exact values erfc(2) = 0.004677735... and erfc(4) = 0.00000 00154 173.... Is
the asymptotic expansion convergent? [Hints: Note that the function -2t (which is part of the
exponent in the exponential e in the second integral above) has its maximum at an endpoint
of the integration interval. Expand exp (-2) in a power series around the origin.]
-2tx
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