Find Coefficient of x^n in log e (a+bx+cx^2)

[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.)

 

[Werg22]

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

 

[tim_lou]

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

 

[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?

 

[Werg22]

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

 

[Mr.IITIAN007]

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

 

[Werg22]

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

 

[Mr.IITIAN007]

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

 

[Hurkyl]

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

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

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

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