Singular points and residues/Singular points and residues

MathProblemsBank banner

MathProblemsBank banner

Math Problems and solutions

Problem list Free problems

Attention! If a subsection is selected, then the search will be performed in it!

Problem: Find the singular points of the function, examine their type and calculate their residues: \[ f(z)=z^{5} \sin \frac{1}{z^{2}} \text {. } \]

10.2.1 Singular points and residues

1.57 $

Problem: Define the type of the singular point \( z= \) 0 for the function: \[ z^{3} \sin \frac{3}{z^{2}} \text {. } \]

10.2.2 Singular points and residues

1.3 $

Problem: Find all isolated singular points and determine their type. \[ \frac{1}{z\left(e^{z}-1\right)} \text {. } \]

10.2.3 Singular points and residues

1.3 $

Problem: Find residues: \[ \operatorname{Res}_{-3} \frac{z+2}{z(z+3)^{2}} . \]

10.2.4 Singular points and residues

0 $

Problem: Find the singular points of the function, indicate their type and find the residues in them: \[ f(z)=\frac{1}{z^{4}+1} e^{\frac{1}{z+1}}+\frac{\tan ^{2} z}{z} . \]

10.2.5 Singular points and residues

3.13 $

Problem: Find the singular points of the function and indicate their type: \[ f(z)=\frac{1}{z^{2}-1} \sin \frac{1}{2 z+1}+\frac{1}{e^{z}+i} . \]

10.2.6 Singular points and residues

3.13 $