Use Res(f(z). Za) = lim (z-zo)f(2), Res (f(2), za) = (n-1)! im 2-1 (2-zo)" f(2), or Res(f(2), zo) = 2-20 to find the residue at each pole of the given function. (Order the poles from smallest to largest first by real part, then by imaginary part.) f(2)= z = 1 (2²-6z+10)² Pole g(za) h(zo) Residue

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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Question
Q9
Use
Res(f(z), Zo) = lim (z-zo)f(z). Res (f(z). Zo) =
2- 20
Rook
to find the residue at each pole of the given function. (Order the poles from smallest to largest first by real part, then by imaginary
part.)
f(z) =
z =
z =
1
(z²-6z+10)²
Pole
1
-1
g(zo)
(n-1)! 22 dz-12-20) f(z), or Res(f(z), zo) =-
h'(zo)
lim
Residue
Transcribed Image Text:Use Res(f(z), Zo) = lim (z-zo)f(z). Res (f(z). Zo) = 2- 20 Rook to find the residue at each pole of the given function. (Order the poles from smallest to largest first by real part, then by imaginary part.) f(z) = z = z = 1 (z²-6z+10)² Pole 1 -1 g(zo) (n-1)! 22 dz-12-20) f(z), or Res(f(z), zo) =- h'(zo) lim Residue
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