# Talk:Taylor series

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Actually, I think Archimedes should be accredited with the first use of the Taylor series, since he used the same method as Madhava: using an infinite summation to achieve a finite trigonometric result. Liu Hui independently employed a similar method 400 years later, but still about 800 years prior to Madhava's work, although the Wikipedia article on Liu Hui does not reflect this.

In fact, it would have been quite easy for them to perform the same task as Madhava. It isn't difficult to square an arc (albeit in an infinite number of steps) using simple Euclidean geometry. I believe that Archimedes and later Liu Hui were aware of this. Last time I heard about it was at a History and Philosophy of Mathematics conference in 1998 at the Center for Philosphy of Science, University of Pittsburgh. Anyone care to dredge up a reference? 151.204.6.171

## Taylor series with Lagrange and Peano remainders

Why there's nothing about those two remainders in the article?

## Bounding the error

I think "Taylor series" wikipedia page should have a section or link to another wikipedia page, explaining how to bound the error made by the a Taylor polynomial of degree n. — Preceding unsigned comment added by Mredigonda (talkcontribs) 14:08, 19 February 2017 (UTC)

That is the subject of a different article, Taylor's theorem. You have to follow the link to get to that from the relevant section(s) of this article. Sławomir Biały (talk) 14:25, 19 February 2017 (UTC)

## Missing boundary definition

I think it's important to define the initial/boundary values for the generalized binomial coefficients given in the Binomial series section. The current definition only works if ${\displaystyle n>=1}$. What if ${\displaystyle n=0}$ this happens as the summation as the power series starts from ${\displaystyle n=0}$. Aditya 17:15, 25 April 2017 (UTC) — Preceding unsigned comment added by Aditya8795 (talkcontribs)

At n=0 we have an empty product, with value 1. There is no problem. --JBL (talk) 01:10, 26 April 2017 (UTC)

## High-dimension case

I searched for "Taylor expansion" and landed on this page, but was surprised not to see the higher-dimension cases in the article at all. This is just an idea for improvement - I almost certainly don't have time to update it myself. Banedon (talk) 02:26, 7 August 2017 (UTC)

There's the section "Taylor series in several variables", which seems to cover that. Or am I missing something myself? --Deacon Vorbis (talk) 03:31, 7 August 2017 (UTC)
No I think you're correct. My mistake. Banedon (talk) 03:50, 7 August 2017 (UTC)
I renamed the section since it would've avoided the above. I'm OK with someone reverting it, but would like to see another suggestion to avoid the above in that case. Banedon (talk) 07:11, 7 August 2017 (UTC)