/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q25P Find the residues of the followi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Q25P (page 687)

Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.

e2z-1z2atz=0

Short Answer

Expert verified

Hence, the residue of the function at z0=0 is 2.

Step by step solution

01

Given information

The given function is: fz=e2z-1z2.

02

Residue Theorem

If z0 is an isolated singular point of fz. Then the integration of the function within any closed curve C is given by:

鈭�cfzdz=b1路2蟺i

Here, b1 is the residue.

03

Step 3:Find the Residue

Since, z=0 is a pole of higher order of 2.

So, the residue of this type of function is given by:

Resz=z0fz=1n-1!limz鈫�z0dn-1dzn-1fz路z-z0n

According to the question, we have:z0=0andn=2

Now, the residue atz0=0will be:

Resz=0fz=12-1!limz鈫�0d2-1dz2-1e2z-1z2路z-02=11!limz鈫�0ddze2z-1=limz鈫�02e2z=2

Hence, the residue of the function at z0=0 is 2.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Find the real and imaginary parts u(x,y) andv(x,y) of the following functions.

z

Find out whether infinity is a regular point, an essential singularity, or a pole (and if a pole, of what order) for each of the following functions. Find the residue of each function at infinity, zz2+1.

Question: Verify that the given function is harmonic, and find a functionof which it is the real part. Hint: Use Problem 2.64. For Problem 2, see Chapter 2, Section 17, Problem 19.

ln(1+x)2+y2

Using the definition (2.1) of , show that the following familiar formulas hold. Hint : Use the same methods as for functions of a real variable.

26..

Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.

1+cosz(蟺-z)2atz=蟺
See all solutions

Recommended explanations on Physics Textbooks

Force

Read Explanation

Modern Physics

Read Explanation

Quantum Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Mechanics and Materials

Read Explanation

Waves Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.