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Variable power as an axis, nonsense? please comment 
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#1
Nov411, 09:22 AM

P: 344

Hello,
Does anyone know if this makes sense or is usable? I've only been able to describe it through a graph. Instead of the x axis being numbers, being powers of x. Let me clarify  where normally would be x=0,1,2,3... would now be x^0, x^1, x^2, x^3 and the y axis would be values of coefficients in a polynomial / coefficients in a power series. Does anyone know of anything like this? I thought it up yesterday and have been intrigued by it. I don't know how to work with it though. thanks austin 


#2
Nov411, 11:42 AM

P: 800



#3
Nov411, 02:57 PM

P: 344

this would be a log base x though right? The log plots on wiki are in base 10 and other values, but not variables. Does that make a difference?



#4
Nov411, 09:07 PM

P: 800

Variable power as an axis, nonsense? please comment
'x' is just a dummy variable that ranges over the real numbers when you're graphing a function, for example. But the xaxis represents the real numbers. I'm not sure I understand what you mean by saying it consists of variables like x^n. 


#5
Nov611, 09:48 AM

P: 344

The idea is like this: write out a few of the first terms in the power series of sin(x),
then mark your x axis as [itex] x^{0}, x^{1}, x^{2}, x^{3}... [/itex] in place of the integers The coefficients of the power series, [itex]a_{n}[/itex], are the y coordinates. Ordered pairs would be [itex](x^{0},a_{0}), (x^{1},a_{1}), (x^{2},a_{2}) [/itex] and so forth. doing this for sin(x)  the coefficients of the power series are 0, 1, 0, 1/6, 0, 1/120... Where I have used 0's for the coefficients of even powers of x. Plotting this looks like [itex] \frac {sin()}{n!} [/itex] but I have no clue how to interpret what I've done. it does look like if we tried to fit those points, that would be an exact fit. I find it curious that just plotting these coefficients resembles a sine function. Perhaps this could be used somehow to determine the function a power series converges to? (assuming it does converge) The same can be done for the cosine, and the plot looks like cos/n!. any idea about this? thanks austin 


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