What is $\sum\limits_{n>0,\text{ odd}} r^n \sin(nx)$ in terms of $z=re^{ix}$? I tried to write $\sin(nx)={e^{inx}-e^{-inx}\over 2i}$ but then I have a sign problem because the $n$ on the associated $r$ is always $>0$.
Thanks in advance!
What is $\sum\limits_{n>0,\text{ odd}} r^n \sin(nx)$ in terms of $z=re^{ix}$? I tried to write $\sin(nx)={e^{inx}-e^{-inx}\over 2i}$ but then I have a sign problem because the $n$ on the associated $r$ is always $>0$.
Thanks in advance!