- #1

golanor

- 59

- 0

I was trying to look for a possible expansion of the ln function. The problem is, that there is no expansion that can be used in all points (like there is for e, sine, cosine, etc..)

Why do you think that is?

To clarify:

Let's say i do the MacLaurin expansion of ln(x+1):

[tex] x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+\frac{x^5}{5}...+(-1)^{n}\frac{x^n}{n}[/tex]

And around 10:

[tex]\text{Log}[11]+\frac{x-10}{11}-\frac{1}{242} (x-10)^2+\frac{(x-10)^3}{3993}-\frac{(x-10)^4}{58564}+\frac{(x-10)^5}{805255}...[/tex]

Are there any other (smooth) elementary functions which cannot be expanded to a taylor series?