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1. In each case, show that any singular point of the function is a pole. Determine the order m of each pole, and find the corresponding residue B. 3 z+1 z² +2 Z e² (a) (b) (c) ;109(d) z² +9' z-1 2z+1 3±1 3 Ans. (a) m=1, B = 6. (b) m = 1, B = 3; (c) m = 3, B=-16 i (d) m=1, B = ± 2π

1. In each case, show that any singular point of the function is a pole. Determine the order m of each pole, and find the corresponding residue B. 3 z+1 z² +2 Z e² (a) (b) (c) ;109(d) z² +9' z-1 2z+1 3±1 3 Ans. (a) m=1, B = 6. (b) m = 1, B = 3; (c) m = 3, B=-16 i (d) m=1, B = ± 2π

Advanced Engineering Mathematics
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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1. In each case, show that any singular point of the function is a pole. Determine the order m of each pole, and find the corresponding residue B. 3 z+1 z² +2 Z e² (a) (b) (c) ;109(d) z² +9' z-1 2z+1 3±1 3 Ans. (a) m=1, B = 6. (b) m = 1, B = 3; (c) m = 3, B=-16 i (d) m=1, B = ± 2π
Transcribed Image Text:1. In each case, show that any singular point of the function is a pole. Determine the order m of each pole, and find the corresponding residue B. 3 z+1 z² +2 Z e² (a) (b) (c) ;109(d) z² +9' z-1 2z+1 3±1 3 Ans. (a) m=1, B = 6. (b) m = 1, B = 3; (c) m = 3, B=-16 i (d) m=1, B = ± 2π
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