Thanks to Cauchy you will always see more about continuous math than discrete. Lots of people can integrate but few can sum!
]]>its just a bonus we doesnt need to know it
Yikes! They think that if it isn't on some kaboobly doo exam it is not important!
The Taylor series is your best friend in math. It allows us to compute things by turning functions into polynomials. We know very little about functions in general for computation. We know lots of things about polynomials!
When you get a job you will be using Taylor series for mostly everything and why is that unimportant?
]]>Unfortunately they do not teach very much about series to students. They go on and on about convergence and the 2 million tests that determine it. They never go into the all important finding what the series converges to.
]]>Found the same example as our professor gave us, on this page:
en.wikipedia.org/wiki/Laurent_series
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 :-)
Thanks a lot!
]]>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
]]>Those look like Laurent series because they have negative powers?
Check this page it has a better explanation for what you want.
]]>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
If you are trying to expand that around 0 it is called a Mclaurin series instead of a Taylor series.
Also you can say a series converges or does not converge to the function.
In this case that function has a singularity at zero, so you can not expand as a Taylor series but you can expand it as a Laurent series.
]]>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
]]>Is the the function you want to Taylorize?
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:
Yes?
]]>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