Q-13E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

Question:In Problem find the first three nonzero terms in the power series expansion for the product f(x)g(x).

Step-by-Step Solution

Answer

The first three nonzero terms of the product of the given power series are

Step 1: Given non- zero terms for given power series

 For two power series   and  with nonzero radii of convergence, the product is also a power series given by

 where the coefficient is

Step 2: Find non- zero terms for given power series

To find the first three nonzero terms of the product, find the first three nonzero coefficients.

 

In this case,

 For n =0  , we have:

Therefore,is a first nonzero coefficient

For n=1, we have:

Therefore,is a second nonzero coefficient

For n=1, we have:

Therefore, the first three nonzero terms of the product of the given power series are