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Q-9E

Expert-verifiedFound in: Page 434

Book edition
9th

Author(s)
R. Kent Nagle, Edward B. Saff, Arthur David Snider

Pages
616 pages

ISBN
9780321977069

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

** **

The required expansion is._{}

**We know that the power series representation of the sum of two power series, given by _{}is 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**

** **

The sum therefore is given by

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