How to Show that Coefficients of a Power Series for tan(x) are 0 for Even n

[complexhuman]

Hi

Just had a question.

Assuming tan(x) is given by a power series with coefficiants (An). How can it be shown that An = 0 whenever n is even.



Thanks

 

[LeonhardEuler]

I assume you mean a power series centered about x=0. tan(x) is an odd function, i.e. tan(-x)=-tan(x). If it had nonzero coefficients to its even powered terms this could not be the case.

 

[complexhuman]

thanks a lot :)