Hello!(adsbygoogle = window.adsbygoogle || []).push({});

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?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Taylor Expansion of Natural Logarithm

Loading...

Similar Threads - Taylor Expansion Natural | Date |
---|---|

I Taylor expansion of f(x+a) | Nov 1, 2017 |

I Taylor expansions, limits and domains | Sep 20, 2017 |

I Taylor expansion of 1/distance | Sep 1, 2017 |

B Multiterm Taylor expansion | Jul 15, 2017 |

I Taylor expansions and integration. | May 7, 2017 |

**Physics Forums - The Fusion of Science and Community**