计算无穷级数之和 ∑(n=1,∞)x^n sin(πn／a)／n!

elim

题：计算 \(\displaystyle\sum _{n=1} ^\infty \frac{x^n \sin (\frac{\pi n}{a})}{n!}\)

elim

对任意复数\(\,x,\,a(\ne 0),\; x^n\sin{\large\frac{\pi n}{a}}=\large\frac{\big(x e^{i\frac{\pi}{a}}\big)^n-\big(x e^{-i\frac{\pi}{a}}\big)^n}{2i}\)

luyuanhong

elim

谢谢楼上陆老师的解答!