Finding Power Series Representation for arctan(x): Help Needed!

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Homework Help Overview

The discussion revolves around finding the power series representation for the function arctan(x). Participants are exploring the relationship between arctan(x) and its integral representation, as well as the series expansion of related functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss starting from the integral representation of arctan(x) and consider the power series of the function 1/(1 + x^2). There are suggestions to differentiate and evaluate at specific points to derive the series.

Discussion Status

The conversation is ongoing, with some participants providing hints and guidance on how to approach the problem. There is a focus on the left-hand side of the equation, with multiple interpretations being explored without a clear consensus on the next steps.

Contextual Notes

Participants express a desire for assistance while indicating a lack of clarity on how to proceed from the integral form. There are references to the need for calculus knowledge, but also suggestions that it may not be necessary for finding the power series.

teng125
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may i know how to solve this ques:find the power series representation for arctan (x)

i know that arctan (x) = integ 1/(1 + x^2) but then from here i don't know how to continue.
pls help...
 
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It seems to me if you're looking for the power series of the thing on the left hand side, then you might want to try looking for the power series of the thing on the right hand side.
 
ya I'm looking for the thing on the left hand side...pls help
 
Take the thing on the right, and differentiate it a few times, and let x = 0 each time.

[tex]f(x) = f(0) + xf'(0) + \frac{x^2}{2!}f''(0) + ...[/tex]

Where f'(0) represents the derivative at x = 0. f''(0) is the second derivative etc. This will give a power series, then you can integrate term by term for the inverse tan function.
 
One doesn't need to know any calculus at all to find the power series for [itex]1/(1+x^2)[/itex].


ya I'm looking for the thing on the left hand side...pls help
I gave you a big hint -- have you not tried to do anything with it?
 
teng125 said:
ya I'm looking for the thing on the left hand side...pls help

Go back and read Hurkyl's reply again!
Hurkyl said:
It seems to me if you're looking for the power series of the thing on the left hand side, then you might want to try looking for the power series of the thing on the right hand side.
 

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