1
vote
3answers
114 views

Precise differences in meaning of Power Series, Taylor Series

Being an physicist/artist, not a real mathematician, I often toss around the terms "Taylor Series" and "Power Series" without any concern. Are these terms be considered interchangeable by ...
3
votes
1answer
41 views

Taylor polynomial and degree

I read that one can form Taylor polynomials for some functions, like $$\sin x\approx x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!}.$$ Is it correct to say that $\sin x$ has no Taylor polynomial ...
6
votes
2answers
298 views

Why does Maclaurin get his own polynomial?

Why is a Taylor polynomial centered around $0$ called a Maclaurin polynomial? It's only a special case of the Taylor polynomial, and it is calculated the exact same way as a Taylor polynomial centered ...