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Yes we doesnt even have exams from Taylor series, we are examined from derivatives, integrations, and limits. Nothing about series just really some basics of infinite series, but nothing more, but hopefully theres lots of information on internet, and lots of helpful people like you who can help people to solve and understand things :-)
Yikes! They think that if it isn't on some kaboobly doo exam it is not important!
Yes thats true, our professor just a little bit explained us Taylor series and told us that its just a bonus we doesnt need to know it, but who wants to know more about series should do this exercise, and gave us this function, and i just found that series are a very interesting theory,
Yes you are right, This function has laurent series but becuase it is defined in 0 too as 0 then the Laurent series converges into the function except in the f(0)=0 there it never converges,
Tanks for helping me with a solution and also helping me in my self-learning, yesterday i was totally confused about series(we learn just taylor at university) but now i hopefully know something about them :-)
When it has been defined as 0? Then it is 0 but it's Taylor series does not represent e^(- 1 / x^2 ). That is what they are saying about a third of the way down the page. I would say 0 does not have a Laurent series. That is the best I can understand it.
Okay now i hopefully understand it after reading the link yo usent me and also something about Laurent series, So if im right the function has some singularity point then it needs Laurent series,
I thought the taylor series for this function are(on image)
Its this function:
i wanted to say if x is 0 then the f(x) is 0 and if x is not 0 then the f(x) is the one above
Our professor of math told me that the taylor series arent same as this function, but he didnt explain me why and how. He told me a hint to proof that this function and its taylor series arent same should be to make sme basic derivation npot for numbers but globally for n. which is pretty hard and im not sure this way i cna make the proof that the taylor series arent same as the function
By taylor series not being same as function i mean that usually if you derivate your taylor series its looking more and more like the function from derivation to derivation and in n infinite derivation it should be same as the function, and in this function it doesnt work, its taylor series doesnt going to look like the function
Hope wrote it easy to understand :-) and hope i havent made any theoretical mistakes
That is x factorial on the end? This is highly unlikely that you would be asked for the Taylor series of such a function.
It is more likely this is what you want: