# MacLaurin Series

1. Mar 7, 2008

### soul

Today, we're taught that MacLaurin series is just another name for Taylor series at x = 0. Then what is the speciality of it? Why doesn't x = 1 or x = 2 have a special name?

2. Mar 7, 2008

### Manchot

Mostly historical reasons.

3. Mar 7, 2008

### matticus

the same reason why the log base e is called the natural/naperian logarithm and all the others are just log base b.

4. Mar 7, 2008

### RESmonkey

It's just easier to write polynomial approximations centered at x=0. Centering them at something else would make (x-a), where a is some shift other than zero (zero would be maclaurin, and so it wouldn't be written).

5. Mar 7, 2008

### John Creighto

Not ture. The difference between a MacLaurin series and a taylor series is that a Maclaurin series can have terms of the form 1/z^n. It depends upon the order of the poles at the point you find the series expansion.

6. Mar 8, 2008

### d_leet

I believe that you are thinking of a Laurant series.

7. Mar 8, 2008

### John Creighto

Oh, maybe so. It's been too long sense I have taken a course in complex variables.