Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 8: Q-9E (page 434)

Question : find the power series expansionfor given the expansions for f(x) and g(x).

Short Answer

Expert verified

The required expansion is.

Step by step solution

01

Find the sum of functions

We know that the power series representation of the sum of two power series, given byis simply obtained by term-wise addition:

For the given series

In order to obtain sum we need to change the index of function g(x)

Let z=n-1=n=z+1

Since index is just a dummy variable, we can replace z with n; the series g(x) thus becomes

02

conclusion

The sum therefore is given by

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

In problems 1-6, determine the convergence set of the given power series.∑n=0∞2-nn+1(x-1)n

Aging spring. As a spring ages, its “spring constant” decreases on value. One such model for a mass-spring system with an aging spring is mx"(t)+bx'(t)+ke- ηtx(t)=0 .

Where m is the mass, b the damping constant, k and η positive constants and x(t) displacement of the spring from equilibrium position. Let m=1 kg, b=2 Nsec/m, k=1 N/m, η =1 sec-1. The system is set in motion by displacing the mass 1m from it equilibrium position and releasing it (x(0)=1, x'(0)=0). Find at least the first four nonzero terms in a power series expansion of about t=0 of displacement.

Find at least the first four nonzero terms in a power series expansion of the solution to the given initial value problem,x'+(sint)x=0;x(0)=1

In Problems 21-28, use the procedure illustrated in Problem 20 to find at least the first four nonzero terms in a power series expansion about’s x=0 of a general solution to the given differential equation.

y"-(sin x)y=cos x

In Problems 29 and 30 use (22) or (23) to obtain the given result.

\({J_0}(x) = {J_{ - 1}}(x) = {J_1}(x)\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

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.

Sign-up for free