# finding the residue

• May 12th 2010, 07:28 PM
fredrick08
finding the residue
g(z) and h(z) are analytic, g'(z0)=h''(z0)not=0 but h(z0)=h'(z0)=0 show that the ration function g(z)/h(z) has a pole of order 2 and the residue is

(2g'/h'')-(2gh'''/3(h'')^2)=b_-1

g(z)=a0+a1(z-z0)+a2(z-z0)^2+....

1/h(z)=(b_-1/(z-z0)^2)+b0/(z-z0)+b1+....

g/h=(a0*b_-1/(z-z0)^2)+a1*b0+a2b1(z-z0)^2+....

so the res is at a0*b_-1?? if this is ok, then from here i have no idea... i must have to differentiate something 3 times but idk, can anyone plz help?
The text passage is a complex analysis problem discussing the residue of a function at a pole. It provides a specific scenario involving analytic functions and their derivatives, and asks for the residue of a particular function.
single_question_with_answer

the passage contains a single mathematical question about finding the residue of a function given certain conditions. an answer is provided in the form of a formula for the residue, and the poster attempts to work through the problem, suggesting they have an idea of the solution but are unsure of the steps to complete it.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# finding the residue

• May 12th 2010, 07:28 PM
fredrick08
finding the residue
g(z) and h(z) are analytic, g'(z0)=h''(z0)not=0 but h(z0)=h'(z0)=0 show that the ration function g(z)/h(z) has a pole of order 2 and the residue is

(2g'/h'')-(2gh'''/3(h'')^2)=b_-1

g(z)=a0+a1(z-z0)+a2(z-z0)^2+....

1/h(z)=(b_-1/(z-z0)^2)+b0/(z-z0)+b1+....

g/h=(a0*b_-1/(z-z0)^2)+a1*b0+a2b1(z-z0)^2+....

so the res is at a0*b_-1?? if this is ok, then from here i have no idea... i must have to differentiate something 3 times but idk, can anyone plz help?
user
The text passage is a complex analysis problem discussing the residue of a function at a pole. It provides a specific scenario involving analytic functions and their derivatives, and asks for the residue of a particular function.

TYPE: SINGLE_QUESTION_WITH_ANSWER

The passage contains a single mathematical question about finding the residue of a function given certain conditions. An answer is provided in the form of a formula for the residue, and the poster attempts to work through the problem, suggesting they have an idea of the solution but are unsure of the steps to complete it.