How to represent a periodic function using Taylor series

[PainterGuy]

Hi,

Is this possible to represent a periodic function like a triangular wave or square wave using a Taylor series? A triangular wave could be represented as f(x)=|x|=x 0<x<π or f(x)=|x|=-x -π<x<0. I don't see any way of doing although I know that trigonometric series could be used instead.

This is not a homework question so I don't think I was supposed to use the template. If my question doesn't fit in this section, please move it to relevant section. Thank you for your help.

 

[Dick]

Hi,

Is this possible to represent a periodic function like a triangular wave or square wave using a Taylor series? A triangular wave could be represented as f(x)=|x|=x 0<x<π or f(x)=|x|=-x -π<x<0. I don't see any way of doing although I know that trigonometric series could be used instead.

This is not a homework question so I don't think I was supposed to use the template. If my question doesn't fit in this section, please move it to relevant section. Thank you for your help.

You can represent periodic function like sine and cosine with Taylor series - so being periodic doesn't make it impossible. On the other hand a triangular wave isn't even differentiable - so no on that one.