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Q-9E

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Fundamentals Of Differential Equations And Boundary Value Problems
Found in: Page 434
Fundamentals Of Differential Equations And Boundary Value Problems

Fundamentals Of Differential Equations And Boundary Value Problems

Book edition 9th
Author(s) R. Kent Nagle, Edward B. Saff, Arthur David Snider
Pages 616 pages
ISBN 9780321977069

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Short Answer

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

The required expansion is.

See the step by step solution

Step by Step Solution

Step 1: 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

Step 2: conclusion

The sum therefore is given by

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