In general, why do we say that the Taylor series of sines and cosines are also Laurent series despite of the power of $z$?
2026-03-31 20:06:17.1774987577
Taylor vs Laurent series - cosines and sines
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The $2n+1$ in the exponent in the series expansion for $\sin$ is a shorthand, since $$ \sin z = \sum_{j=0}^\infty \frac{\sin^{(j)}(0) z^j}{j!} $$ the coefficients $\sin^{(j)}(0)/j!$ evaluates to $0$ when $j$ is even, hence they can be skipped.