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

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    Logarithmic Series
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Homework Help Overview

The discussion revolves around finding the coefficient of x to the power n in the expansion of log e (a + bx + cx²), where a, b, c, and n are real numbers. Participants are exploring various mathematical techniques related to series expansions and logarithmic functions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants mention using Taylor expansion and the Binomial theorem, but express frustration with the complexity of the resulting expressions. Some suggest factoring and taking derivatives, while others inquire about the expansion of 1/x as a potential approach.

Discussion Status

The discussion is ongoing, with participants sharing different methods and expressing challenges in simplifying their results. There is a recognition of the need for clarification and verification of techniques, but no consensus has been reached on a specific approach or solution.

Contextual Notes

Participants note that they are encountering difficulties with the expansions and are seeking more straightforward methods. There is an emphasis on adhering to forum policies regarding the sharing of final answers.

Mr.IITIAN007
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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.)
 
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Using the Taylor expansion and the Binomial theorem gives an ugly expression...
 
factor and take derivative. then expand using geometric series. integrate afterward.
 
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?
 
Is there an expansion of 1/x? If so, you could easily do it for a + bx + cx2 that has real solutions.
 
O.K.I will try that.Werg22 , Please give me the final answer so that I can verify it.
 
I actually do not know of the expansion of 1/x...
 
Use binomial expansion of (0 + x) to the power -1.
 
Werg22 said:
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.

Mr.IITIAN007 said:
O.K.I will try that.Werg22 , Please give me the final answer so that I can verify it.
It's against our policy to hand out answers.
 

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