{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW10.EGM4313

# HW10.EGM4313 - Page 657 problem 9 β«z C dz =β β1 C 2 1...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Page 657, problem 9: β«z C dz =β« β1 C 2 1 z β 1dz = 2Οi 1 = βΟ i z +1 β1 β1 Page 657, problem 15: β« C Ln( z β 1) dz = 2Ο i β ln ( 4 ) z β5 Page 672, problem 21: Convergent, but not absolutely convergent. Real and imaginary parts satisfy the alternating sign test. Page 677, problem 9: ( n β i) n β β as n β β β Radius of convergence =0. Page 677, problem 11: ( β 1) n+1 lim ( β 1n) n ββ n+2 = lim n ββ n +1 = 1 β Radius of convergence = 1. Center is at z=0. n n +1 Page 682, problem 3: Center is at z=-i. lim n ββ n 2n = 2 β R 2 = 2 β R = 2 n +1 2 n +1 I donβt see any advantage to integrating or differentiating to get an easier convergence problem so feel free to do either. Page 682, problem 4: ( β 1) n lim (2n )+ 1 β1 n ββ n +1 =1β R = Ο 2n + 3 β z Differentiate series to get β ( β 1) Ο n =1 2n n β R = Ο by inspection. Page 690, problem 8: f ( z ) = Ln(1 β z ) β f ( n ) ( z ) = β ( n β 1)! (1 β z ) n β β f ( z ) = Ln(1 β i ) + β n =1 Radius of convergence = distance from i to 1 = β1 (1 β i ) n n ( z β i) n 2. Page 707, problem 9: 1 1 1 1 β ( β 1) f ( z) = 2 = = β 2 n+1 i n+1 ( z β i ) n z + 1 z β i z + i z β i n =0 n Closest singularity at z=-i, implies R=2. Page 707, problem 15: 1 = 1 + z 3 + z 6 + z 9 + β β β, z < 1 3 1β z Let w=1/z. 1 1 1 1 1 1 1 = = βw3 = β w 3 β w 6 β w 9 β β β β = β 3 β 6 β 9 β 12 β β β β, z > 1. 3 3 1 1β z z z z z 1β w 1β 3 w ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

HW10.EGM4313 - Page 657 problem 9 β«z C dz =β β1 C 2 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online