Let n e N. You are going to prove that 1.3-5.. (2n – 1) = 27 2 -4 ·6 . .· (2n) 27 In := | cos2" 0 d0 (a) Relate In to the following integral (++) 2n Jn := {lz|=1}
Let n e N. You are going to prove that 1.3-5.. (2n – 1) = 27 2 -4 ·6 . .· (2n) 27 In := | cos2" 0 d0 (a) Relate In to the following integral (++) 2n Jn := {lz|=1}
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please type full worked solution.
Please do part a. Will post separate questions for parts b, c and d
![Let n e N. You are going to prove that
1.3-5.. (2n – 1)
= 27
2 -4 ·6 . .· (2n)
27
In :=
| cos?" 0 do
(a) Relate In to the following integral
2n
:=
{l2|=1}
1
(b) For an appropriate zo € C and an appropriate analytic function f(z), write Jn in the
form
{(2)
dz .
(c) Using the Cauchy Integral Formula, show that
f(2)
2in
g(2n) (z0) .
(2n)!
dz =
=|=1}
I+uz(0z – 2)
(d) Put together the above pieces to obtain the value of In.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F348082f4-b121-4ba4-892a-9b3ad6631b87%2Fb669bf0a-36c1-414d-b3e6-c5ecb73a79b2%2Fd1fuls_processed.png&w=3840&q=75)
Transcribed Image Text:Let n e N. You are going to prove that
1.3-5.. (2n – 1)
= 27
2 -4 ·6 . .· (2n)
27
In :=
| cos?" 0 do
(a) Relate In to the following integral
2n
:=
{l2|=1}
1
(b) For an appropriate zo € C and an appropriate analytic function f(z), write Jn in the
form
{(2)
dz .
(c) Using the Cauchy Integral Formula, show that
f(2)
2in
g(2n) (z0) .
(2n)!
dz =
=|=1}
I+uz(0z – 2)
(d) Put together the above pieces to obtain the value of In.
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