# Homework Help: Logarithmic series

1. May 19, 2007

### Mr.IITIAN007

Find the coefficient of x to the power n in the expansion of

log e ( a + bx + cx2 ) where a,b,c,n belong to R.

(Note: cx2 means it is c x (X square ) and e is base for which the above logarithm is defined.)

2. May 19, 2007

### Werg22

Using the Taylor expansion and the Binomial theorem gives an ugly expression...

3. May 19, 2007

### tim_lou

factor and take derivative. then expand using geometric series. integrate afterward.

4. May 20, 2007

### Mr.IITIAN007

Werg22 and tim_lou thanks.But guys!!!!! I have already tried those techniques but I have not got an accurate to the point answer.As Werg22 says I am getting an ugly expansion of no significance.I am still far away from getting a simplified answer.Tim_lou, if you are getting a simplified answer then what is it?????????

5. May 21, 2007

### Werg22

Is there an expansion of 1/x? If so, you could easily do it for a + bx + cx2 that has real solutions.

6. May 21, 2007

### Mr.IITIAN007

O.K.I will try that.Werg22 , Please give me the final answer so that I can verify it.

7. May 21, 2007

### Werg22

I actually do not know of the expansion of 1/x...

8. May 22, 2007

### Mr.IITIAN007

Use binomial expansion of (0 + x) to the power -1.

9. May 22, 2007

### Hurkyl

Staff Emeritus
1/x is the (only Laurent) expansion for 1/x about the point x = 0.

It's against our policy to hand out answers.