Generating McLaurin Series for ln (1+x^2)

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SUMMARY

The discussion focuses on generating the Maclaurin series for the function ln(1+x^2). The user seeks assistance in deriving this series, referencing the known Maclaurin series for ln(1+x). The solution involves differentiating ln(1+x) repeatedly and substituting x with x^2 to obtain the desired series. HallsofIvy provides guidance on this method, confirming its effectiveness.

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  • Understanding of Maclaurin series expansion
  • Familiarity with differentiation techniques
  • Knowledge of logarithmic functions
  • Basic calculus concepts
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islandboy401
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I am having trouble generating a MacLaurin Series for

ln (1+x^2)

Please help me out on this.
 
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Do you know the McLaurin series for ln(1+ x)? If not, it's easy to differentiate that repeatedly and just using the definition of McLaurin series. Once you have that, replace x with x2.
 
Thank you very much HallsofIvy...
 

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