Radius of convergence

**Haris** · January 22nd 2009, 11:09 AM

What would be the radius of convergence of $e^{sinx}$ ?

**Mathstud28** · January 22nd 2009, 11:18 AM

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?

**Haris** · January 22nd 2009, 11:20 AM

Aye, sorry thats the question I wanted to ask.

**Mathstud28** · January 22nd 2009, 11:25 AM

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 $0<e^x<1$ iff $x<0$ . So in our case we need $\sin(x)<0$ or that $\pi<x<2\pi$ or $3\pi<x<4\pi$ or in general $(2n-1)\pi<x<2n\pi~~n\in\mathbb{Z}$

Thread: Radius of convergence

LinkBack

Thread Tools

Display

Radius of convergence

Similar Math Help Forum Discussions

investigate the convergence at the radius of convergence

Radius of convergence; Interval of convergence.

radius of convergence and interval of convergence of the series

Find the radius of convegence and the radius of convergence

series convergence and radius of convergence

Search Tags