# Thread: taylor series expansion of exp^sinx

1. ## taylor series expansion of exp^sinx

Hi,

I need to expand e^sin(x)

I have used the series for e^x and am trying to exapnd out the sin terms.

I get

1 + (x-....) + (1/2!)*(x-...)^2 + (1/3!)*(x-...)^3

and want to simplify.

Is 1 + x + (1/2!)*x^2 + (1/3!)*x^3 + ... the right simplification?

2. Originally Posted by Roland25
Hi,

I need to expand e^sin(x)

I have used the series for e^x and am trying to exapnd out the sin terms.

I get

1 + (x-....) + (1/2!)*(x-...)^2 + (1/3!)*(x-...)^3

and want to simplify.

Is 1 + x + (1/2!)*x^2 + (1/3!)*x^3 + ... the right simplification?
If you are only interested in the first few terms rather than the general term, then you can use the definition of the Taylor series since $\exp(\sin(x))$ is easily differentiated a few times.

CB

3. I understand that, as thats one of the first things I did, but I'm after a simplified answer. I was just wondering if what I had writen was a feasible approximation or not when you expanded out the sin's