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while writing a Taylor series
while writing a Taylor series expansion I think we should be careful about two things, whether the point about which we are expanding is analytic and the radius of convergence. But in most of the times we just check the differentiability of the function about the point of expansion rather than the analyticity of the function at that point.It works in most of the cases.Is it a dangerous practice?
Your comment that one should
Your comment that one should check analytic property and radius of convergence is absolutely correct.
If attention is not paid to these point one may end up with answers which may not make sense,