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#1 2011-05-10 10:21:47

bobbym
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Numerical method for radius of convergence.

Hi;

Here is an interesting numerical means to compute the radius of convergence. It requires that the coefficients of x^n , alternate or are all the same sign.





We need to compute the ordered pairs:



The above generates:



Extrapolate the value in the second column for n = ∞. Looks like we get -.5625.



Here is another one:









This one is a little tougher we must extrapolate to 1 / ∞. So you do a linear fit of the last two points. You get:



The limit of that as x approaches 0 is obviously .2498259



Which is close to the the exact answer of 2.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
 

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