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#1 2007-09-06 09:57:07

bossk171
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Registered: 2007-07-16
Posts: 305

1+x+x^2+x^3+...

Does the series

Have a set variable like the Zeta function or the Gamma function?

Like


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#2 2007-09-06 19:18:36

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: 1+x+x^2+x^3+...

What is "set variable"?

For the series to be convergent, is't nessesary x to be in the unary complex circle: Abs(x)<1.

Last edited by krassi_holmz (2007-09-06 19:19:24)


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#3 2007-09-07 01:53:21

bossk171
Member
Registered: 2007-07-16
Posts: 305

Re: 1+x+x^2+x^3+...

By set variable, I mean a letter that denotes that function universally. If I tell you about a function "f" I could be talking about any function I've made up, but if I tell you about the Gamma function, you know exactly what I'm talking about. Does this infinite series have a "name" that everyone knows?


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#4 2007-09-07 05:06:08

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: 1+x+x^2+x^3+...

We don't need a special function, because it's

when convergant.


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#5 2007-09-07 05:55:54

bossk171
Member
Registered: 2007-07-16
Posts: 305

Re: 1+x+x^2+x^3+...

That's actually why I asked. I'm trying to keep a notebook of Math I know, in case I ever need to go back and find a proof for something, I'll have it written down. I was writing up the proof that:

When I noticed that it'd be easier to do if I had a name for the function. For example, if I say that:

Then it's easy to show that

but easier to write:

Solving for S(X) gives:

With out defining S(x) it becomes very tedious to write. I was just wondering if I should use S in my notes or if there was a commonly use letter to denote it.


There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

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#6 2007-09-07 07:30:58

krassi_holmz
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Registered: 2005-12-02
Posts: 1,905

Re: 1+x+x^2+x^3+...

If you use it very fraquently, you can write in the beginning "S(x) stands for..." and then use it.
I've seen a notebook with properties of the arctangens function, written 'A' for short.


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