Deriving the Power Series of Arctan through Integration

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Discussion Overview

The discussion revolves around deriving the power series of the arctangent function through integration. Participants express confusion about the process and seek clarification on the steps involved, particularly in relation to Taylor series.

Discussion Character

  • Exploratory, Homework-related

Main Points Raised

  • One participant asks for a step-by-step explanation of deriving the power series for arctan through integration, indicating a lack of understanding.
  • Another participant provides a partial mathematical expression related to the derivative of arctan, suggesting a connection to the power series expansion of the function.
  • A third participant encourages the original poster to explore Taylor series, referencing an external link for additional information.

Areas of Agreement / Disagreement

Participants generally express confusion about the derivation process, and no consensus or resolution is reached regarding the steps involved in deriving the power series.

Contextual Notes

The discussion lacks detailed mathematical steps and specific assumptions that may be necessary for a complete understanding of the derivation process.

hivesaeed4
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How do we get the power series of arctan using integration. Could someone explain this step by step as I'm quite confused about it.
 
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hivesaeed4 said:
How do we get the power series of arctan using integration. Could someone explain this step by step as I'm quite confused about it.


[itex]\frac{1}{1+x^2} = 1-\frac{x^2}{2!}+\frac{x^4}{4!}-...[/itex], and since

[itex](Arctan\, x)'=\frac{1}{1+x^2}[/itex] , then...

DonAntonio
 
hivesaeed4 said:
How do we get the power series of arctan using integration. Could someone explain this step by step as I'm quite confused about it.

Hey hivesaeed4 and welcome to the forums.

To add on to what DonAntonio said, investigate what Taylor series are and how are they are used:

http://en.wikipedia.org/wiki/Taylor_series
 
Thanks. Thanks a lot.
 

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