# I The a in Taylor series

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1. Jul 22, 2016

### abdo799

i watched a lot of videos and read a lot on how to choose it, but i what i can't find anywhere is, what's the physical significance of the a, if we were to draw the series, how will the choice of a affect it?

2. Jul 22, 2016

### BvU

What a ? We at PF are bad at telepathy, so we need an example or something to guess what you mean with a...

3. Jul 22, 2016

### Staff: Mentor

Variable names are arbitrary. You can call everything you want "a".

Sometimes it is possible to guess what is meant if everyone uses the same variable names, but that is not the case here.

4. Jul 22, 2016

### BvU

actually, in a flash of telepathic insight ( and googling 'taylor series' ) I'm almost sure what abdo means, but rewarding bad practice isn't good practice ...

5. Jul 22, 2016

### Erland

Probably, Abdo means the $a$ in the representation $f(x)=\sum_{n=0}^\infty c_n(x-a)^n$. This $a$ is simply the point about which the expansion is taken. The sum will be different, and will perhaps not converge, if we change this point.

For example, expanding $e^x$ about $0$ gives $e^x=\sum_{n=0}^{\infty}x^n/n!$ but expanding about $1$ gives $e^x=\sum_{n=0}^{\infty}e(x-1)^n/n!$

6. Jul 22, 2016

### wrobel

he perhaps means this "a":

7. Jul 22, 2016

### abdo799

hahahahhahaha, sry, it's just that everybody calls the center of the series a, nice video though :D

8. Jul 22, 2016

### abdo799

u see, this is what i love about PF, everybody is friendly enough to joke about it if i made a mistake instead of keep reporting me or removing the thread

9. Jul 22, 2016

### Staff: Mentor

If the series converges to the function everywhere ("infinite" radius of convergence), then the full taylor series is the same everywhere, although the terms look differently - so if you just take a few of them, the approximation will look differently. Typically the approximation is good close to "a".

If the series does not converge to the function everywhere, it can look completely different for different "a".

10. Jul 22, 2016

### Ssnow

Without a this the Tylor series and we don't have informations on it ....

ok, it is a stupid joke. As said before I agree assuming $a$ the center of the Taylor series. Physical interpretation is that around $a$ you can approximate, well as you want, your function by a polynomial expressions .. This is good because polynomials are simple to treat instead other functions ...

11. Jul 22, 2016

### Staff: Mentor

I denote it by $x_0$ or when lazy $c$ for centre. So you are wrong, not everybody calls it $a$.

12. Jul 22, 2016

### Erland

I don't get it. What "a"?

13. Jul 22, 2016

### wrobel

the aria of the black haired guy consists only of "a-a-a-a-a"