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If f(x) has a power series: a_n(x-a)^n (centered at a)
what does the power series for f(2x) look like?
what does the power series for f(2x) look like?
If f(x) has a power series: a_n(x-a)^n (centered at a)
what does the power series for f(2x) look like?
I would think he is after something like this:
[tex]f(2x) = \sum_{n=0}^{\infty}a_n(2x-a)^n = \sum_{n=0}^{\infty}a_n2^n\left(x-\frac a 2\right)^n =\sum_{n=0}^{\infty}b_n\left(x-\frac a 2\right)^n[/tex]
where [itex]b_n=a_n2^n[/itex]