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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 :-)
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,
Found the same example as our professor gave us, on this page:
en.wikipedia.org/wiki/Laurent_seriesTanks 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 :-)
Thanks a lot!
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,
The function
has singularity in 0 but when we define the function in x=0 that it is 0. Now we have a function which is defined everywhere, in this case it is still for a Laurent series?Thanks
I thought the taylor series for this function are(on image)
So theres no taylor series for this function? And just laurent series?
Because the question was, give me a proof that taylor series of this function doesnt converges into the function so the answer is it has no taylor series so they couldnt converge into the function if they not exist?
I need to look deeper into laurent series, have read about them just a little bit,
Thanks for all your help and corrections
Rick
Slovakia
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
Hello,
First sorry for my english, i'm not good in it.
i've got a little problem when learning Taylor Series,
Somewhere i read that the n derivation of a function is same as n derivation of functions taylor series but that here are few excuses.
For example this function f(x)=0 x=0, f(x)=e^−(1/x^2) x!=0 is supposed to doesnt equal its taylor series? Is there any proof or explanation for it?
Thanks a lot
Calculus beginner
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