• January 22nd 2009, 11:09 AM
Haris
What would be the radius of convergence of $e^{sinx}$?
• January 22nd 2009, 11:18 AM
Mathstud28
Quote:

Originally Posted by Haris
What would be the radius of convergence of $e^{sinx}$?

This is not a question? What does this mean?

What is the ROC of $\sum_{n=0}^{\infty}e^{n\sin(x)}$ maybe?
• January 22nd 2009, 11:20 AM
Haris
Aye, sorry thats the question I wanted to ask.
• January 22nd 2009, 11:25 AM
Mathstud28
Quote:

Originally Posted by Haris
Aye, sorry thats the question I wanted to ask.

This is just a geometric series, so we need the absolute value of the ratio, $e^{\sin(x)}$ in this case, to be less than one.

So this series converges for all values of x in the set $S=\left\{x:|e^{\sin(x)}|=e^{\sin(x)}<1\right\}$

Note that we have that $0 iff $x<0$. So in our case we need $\sin(x)<0$ or that $\pi or $3\pi or in general $(2n-1)\pi