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Discuss the type of singularity (removable, pole and order, essential, branch, cluster, natural barrier, etc.); if the type is a pole give the strength of the pole, and give the nature (isolated or not) of all singular points associated with the following functions. Include the point at infinity. (a) e²² z² 1 (b) e²-1 z² (c) etanz (d) z³ z²+z+1

Discuss the type of singularity (removable, pole and order, essential, branch, cluster, natural barrier, etc.); if the type is a pole give the strength of the pole, and give the nature (isolated or not) of all singular points associated with the following functions. Include the point at infinity. (a) e²² z² 1 (b) e²-1 z² (c) etanz (d) z³ z²+z+1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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1. Discuss the type of singularity (removable, pole and order, essential, branch, cluster, natural barrier, etc.); if the type is a pole give the strength of the pole, and give the nature (isolated or not) of all singular points associated with the following functions. Include the point at infinity. (c) etan z (d) (e) (a) 2¹/3 ez² z² 1 z-1 1 Tuvics 101 seluun J.J 1 (b) 3.5 Singularities of Complex Functions e²z - 1 z² (f) log(1+z¹/²) (g) f(z) = (h) f(z) = Σ n=1 n! (i) sech z z³ z²+z+1 z² |Z| ≤ 1 1/z² |z| > 1 {₁} (j) coth 1/z 157
Transcribed Image Text:1. Discuss the type of singularity (removable, pole and order, essential, branch, cluster, natural barrier, etc.); if the type is a pole give the strength of the pole, and give the nature (isolated or not) of all singular points associated with the following functions. Include the point at infinity. (c) etan z (d) (e) (a) 2¹/3 ez² z² 1 z-1 1 Tuvics 101 seluun J.J 1 (b) 3.5 Singularities of Complex Functions e²z - 1 z² (f) log(1+z¹/²) (g) f(z) = (h) f(z) = Σ n=1 n! (i) sech z z³ z²+z+1 z² |Z| ≤ 1 1/z² |z| > 1 {₁} (j) coth 1/z 157
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