How do I determine if a function is analytic at x=a?

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Homework Statement


I'm studying diff eq and I'm not sure how to show that a function is analytic at point x=a. I know that the definition says that a function p(x) is analytic if it has a Taylor series expansion at x=a, but not sure how to show it.

Thank you for the help!

Homework Equations


The Attempt at a Solution

 
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