Is this valid?

• Jan 31st 2009, 07:52 AM
godofgods
Is this valid?
I was just messing around, and wondering is what I've done valid. I made this up myself - but that's not to say it doesn't already exist. It has to do with series expansions.

Let W be an integration from 0 to x.

We^x = e^x -1
1 = e^x - We^x
1 = (1-W)e^x
1/(1-W) = e^x

Using this we can get that e^x = (1 + W + W^2 + W^3 + ... + W^n), which is (1 + W + W^2/2! + W^3/3! + ... + W^n/n!)

Is this a valid form of getting a series expansion? Is there a problem somewhere? And, is there a name for it?

Thanks.
• Jan 31st 2009, 10:39 AM
Jester
Quote:

Originally Posted by godofgods
I was just messing around, and wondering is what I've done valid. I made this up myself - but that's not to say it doesn't already exist. It has to do with series expansions.

Let W be an integration from 0 to x.

We^x = e^x -1
1 = e^x - We^x
1 = (1-W)e^x
1/(1-W) = e^x ***

Using this we can get that e^x = (1 + W + W^2 + W^3 + ... + W^n), which is (1 + W + W^2/2! + W^3/3! + ... + W^n/n!)

Is this a valid form of getting a series expansion? Is there a problem somewhere? And, is there a name for it?

Thanks.

I see a problem here ***. The left side of this equation is an operator while the right side is a function of x.
• Jan 31st 2009, 02:46 PM
godofgods
Quote:

Originally Posted by danny arrigo
I see a problem here ***. The left side of this equation is an operator while the right side is a function of x.

But W, which is an integration from 0 to x with respect to x, is the same as x^n/n!. If you change it to that does it rectify the problem?
• Jan 31st 2009, 04:28 PM
ThePerfectHacker
Quote:

Originally Posted by godofgods
I was just messing around, and wondering is what I've done valid. I made this up myself - but that's not to say it doesn't already exist. It has to do with series expansions.

Let W be an integration from 0 to x.

We^x = e^x -1
1 = e^x - We^x
1 = (1-W)e^x
1/(1-W) = e^x

Using this we can get that e^x = (1 + W + W^2 + W^3 + ... + W^n), which is (1 + W + W^2/2! + W^3/3! + ... + W^n/n!)

Is this a valid form of getting a series expansion? Is there a problem somewhere? And, is there a name for it?

Thanks.

Ignore the $\displaystyle W$ and write it out. What you are saying is that: $\displaystyle 1 = \left( 1 - \int_0^x \right) e^x dx$.
What is that supposed to mean?
That looks strange (Surprised).

Maybe you can do that in physics but you certainly cannot do that in math. (Rofl)