Rotated functions and taylor series If one rotates a function such as the sine function about the origin, is there a general method to find the taylor series for the rotated function? Assuming of course that the rotated function is still a single valued function.
I have limited time to post the answer, but I think this is it.  The individual coefficients get multiplied such that $b_n = a_n\exp(2n\pi i k)$, where k is the rotation angle, some rational or irrational rotational coefficient scaled to be between zero and one, such that $\theta=\exp(2\pi i k)$
I have limited time to post the answer, but I think this is it.  The individual coefficients get multiplied such that $b_n = a_n\exp(2n\pi i k)$, where k is the rotation angle, some rational or irrational rotational coefficient scaled to be between zero and one, such that $\theta=\exp(2\pi i k)$