Function Relations: Seeking Expert Opinion & Resources

[beta23]

I'm very sure this is wrong. I think the f^i(x) should be changed to a g^i(x) where g^i(x) is some function (I'm guessing either Gamma or Beta) and that the infinity sign should be changed to a i-->k where k is some arbitrary value. Reason being f^i(x) will always equal zero and j/i! will also always tend to zero.

Besides that I have absolutely nothing to say about this so I was hoping for some expert opinion and perhaps if you could recommend any reading I could do to better my understanding on the subject.

Thank you!

 

[Orodruin]

I'm very sure this is wrong.

No, you are wrong here. This is nothing but the Maclaurin series (i.e., Taylor series around $x = 0$) for any infinitely differentiable function.

 

[beta23]

No, you are wrong here. This is nothing but the Maclaurin series (i.e., Taylor series around $x = 0$) for any infinitely differentiable function.

Thanks a lot Orodruin. Is there any books you can recommend for the Taylor Series?

 

[PAllen]

Thanks a lot Orodruin. Is there any books you can recommend for the Taylor Series?

So far as I know, every first introduction to calculus has this (including derivation, convergence criteria, etc.)