ziggy/math/eng peopel

[Brood_Star]

i'm stupid

why does the radius of convergence remain unchanged when you differentiate or integrate a power series, even though the interval of convergence/endpoints can change. proof/theorem/explanation/etc?

[TheAmazingKoalaDolphin]

i'm stupid

yep <3

[Brood_Star]

i aint even know what the formal definition of the radius is other than between the two endpoints

i googled it and all i found was some lim sup (beta) problem and that aint very helpful

sorry to reinforce nadota stupidity stereotypes

[TheAmazingKoalaDolphin]

pretty sure it's not a stereotypes.

[Brood_Star]

why yall gotta be so negative all the time

[TheAmazingKoalaDolphin]

why you talk like you're from tennessee?

[Brood_Star]

why u got a koala dolphin avatar

[TheAmazingKoalaDolphin]

because i'm amazing.

why you have to be so hip all the time ?

[Brood_Star]

if you would kindly define hip id be more inclined to respond

im pretty sure u can call anything a hipster these days

[TheAmazingKoalaDolphin]

too lazy to find a definition but these are lyrics from a 1947 song by Harry "The Hipster" Gibson

Hey you know there's a lot of talk going around about this hip and hep jive. Lots of people are going around saying "hip." Lots of squares are coming out with "hep." Well the hipster is here to inform you what the jive is all about.

The jive is hip, don't say hep
That's a slip of the lip, let me give you a tip
Don't you ever say hep it ain't hip, NO IT AIN'T
It ain't hip to be loud and wrong
Just because you're feeling strong
You try too hard to make a hit
And every time you do you tip your mitt
It ain't hip to blow your top
The only thing you say is mop, mop, mop
Keep cool fool, like a fish in the pool
That's the golden rule at the Hipster school
You find yourself talking too much
Then you know you're off the track
That's the stuff you got to watch
Everybody wants to get into the act
It ain't hip to think you're "in there"
Just because of the zooty suit you wear
You can laugh and shout but you better watch out
Cause you don't know what it's all about, man
Man you ain't hip if you don't get hip to this hip and hep jive
Now get it now, look out
Man get hip with the hipster, YEAH! Got to do it!
be hip not hep, coz hep is not hip
so just be hip and pray you dont slip!

this is great i really feel us bonding and becoming closer to each other. hope nobody crashes our intimate exchanges.

[Brood_Star]

aint wanna read it cause i just wanna study but i agree and more importantly hope someone answers the original question

[1300]

S = sum over n of c_n * x^n => r = lim n->inf c_n/c_n+1

d/dx S = sum over n of n * c_n * x^(n-1) => r = lim n->inf n*c_n/((n+1)*c_(n+1)) = lim n->inf c_n/c_n+1

integral S dx = sum over n of c_n * ^(n+1) / (n+1) => r = lim n->inf (c_n/(n+1))/(c_(n+1)/(n+2)) = lim n->inf c_n/c_n+1

all three r's are the same

if you're asking for some fundamental reason then iunno ask some math major

[Brood_Star]

nope, that makes sense

[Applejack]

if you would kindly define hip id be more inclined to respond

im pretty sure u can call anything a hipster these days

http://d24w6bsrhbeh9d.cloudfront.net...48358_460s.jpg

[saga16]

First, you can only differentiate and integrate term by term for certain functions... too lazy to do the proof myself so read:
http://www.dpmms.cam.ac.uk/~agk22/uniform.pdf

Second the complex analysis way of thinking about the radius of convergence is that the radius of convergence is the distance from xo to the nearest singularity in the complex plane. [example: the taylor series for the function f(x) = 1/(x^2+1) has radius of convergence 1 because the nearest singularities in the complex plane are +i and -i which are both one unit from the origin]

what class is this for, complex analysis[it can't be for diffeq cus u already took that]? And why the fuck would you have to take that as an engineering major.

[Brood_Star]

there's a mandatory complex analysis class in 3rd year but it was just a random power series review q

e: are you not an engineer? i just assumed u were from what 5-s told me

[Kanadian]

lmfao is this a real question?

[1300]

First, you can only differentiate and integrate term by term for certain functions... too lazy to do the proof myself so read:
http://www.dpmms.cam.ac.uk/~agk22/uniform.pdf

Second the complex analysis way of thinking about the radius of convergence is that the radius of convergence is the distance from xo to the nearest singularity in the complex plane. [example: the taylor series for the function f(x) = 1/(x^2+1) has radius of convergence 1 because the nearest singularities in the complex plane are +i and -i which are both one unit from the origin]

what class is this for, complex analysis[it can't be for diffeq cus u already took that]? And why the fuck would you have to take that as an engineering major.

ur link doesnt apply, its fucking power series lol
though im sure you can find some cool intuition about this radius of convergence issue with complex analysis

cant comment on it, all i remember doing is a shitton of useless contour integrals

[saga16]

there's a mandatory complex analysis class in 3rd year but it was just a random power series review q

e: are you not an engineer? i just assumed u were from what 5-s told me

Im an engineer but getting a double major in something else[not engineering] that requires tons of stupid math/physics

and 1300 it applies unless im being retarded. although I just realized now I really didn't answer his question.

[ixmike88]

howd u not just come to me brah