What Makes the MacLaurin Series Unique Compared to Other Series?

[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?

 

[Manchot]

Mostly historical reasons.

 

[matticus]

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

 

[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).

 

[John Creighto]

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?

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.

 

[d_leet]

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.

I believe that you are thinking of a Laurant series.

 

[John Creighto]

I believe that you are thinking of a Laurant series.

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