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Thread: ziggy/math/eng peopel

April 15th, 2012, 02:12 AM #1
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ziggy/math/eng peopel
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?

April 15th, 2012, 02:13 AM #2

April 15th, 2012, 02:15 AM #3
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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

April 15th, 2012, 02:17 AM #4
pretty sure it's not a stereotypes.
Spoiler

April 15th, 2012, 02:28 AM #5
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why yall gotta be so negative all the time

April 15th, 2012, 02:31 AM #6
why you talk like you're from tennessee?
Spoiler

April 15th, 2012, 02:32 AM #7
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why u got a koala dolphin avatar

April 15th, 2012, 02:34 AM #8
because i'm amazing.
why you have to be so hip all the time ?Spoiler

April 15th, 2012, 02:40 AM #9
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if you would kindly define hip id be more inclined to respond
im pretty sure u can call anything a hipster these days

April 15th, 2012, 02:46 AM #10
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.Spoiler

April 15th, 2012, 02:48 AM #11
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aint wanna read it cause i just wanna study but i agree and more importantly hope someone answers the original question

April 15th, 2012, 03:12 AM #12
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^(n1) => 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

April 15th, 2012, 03:19 AM #13
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nope, that makes sense

April 15th, 2012, 03:22 AM #14
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April 15th, 2012, 03:46 AM #15
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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.

April 15th, 2012, 04:08 AM #16
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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 5s told meLast edited by Brood_Star; April 15th, 2012 at 04:12 AM.

April 15th, 2012, 04:14 AM #17

April 15th, 2012, 04:24 AM #18
Last edited by 1300; April 15th, 2012 at 04:28 AM.

April 15th, 2012, 11:41 AM #19
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April 15th, 2012, 11:48 AM #20