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saltydog
saltydog is offline
#11
Apr19-05, 07:43 AM
Sci Advisor
HW Helper
P: 1,593
Hello Bomba. Thanks for responding, you too Hurkyl. I know you're just telling me the minimum for my own good but you know what, I couldn't even get past the definition and I'd like to understand it. This is what I have:

If I start from [itex]R_0[/itex] and you say calculate R2, R4, R6,. . ., and the recursion relation is always in reference to R(n-2), then it's just like doing it for each N and set up the relation for R(n-1). Is that not correct? That is, if I start with [itex]R_0[/itex], then it seems to me, just ignore the odd members in the sequence. Perhaps that is not correct though. When I experiment with it though in Mathematica, say for R0=1.9, it doesn't seem to converge to the value you specify. This is how I set it up in Mathematica. Perhaps you can correct my interpretation:

[tex]f[x,xm1]=\sqrt{x+\sqrt{x-\sqrt{xm1}}}[/tex];

[tex]xstart=1.9[/tex]

[tex]ntotal=alargenumber[/tex]

[tex]valist=Table[{0},{ntotal}][/tex]

[tex]valist[[1]]=f[xstart,xstart][/tex]

[tex]For[n=2,n<ntotal,n++,[/tex]

[tex]valist[[n]]=f[xstart,valist[[n-1]]];[/tex]

When I do that, it seems to converge to 1.639 . . .

But:

[tex]\frac{1+\sqrt{4xstart-3}}{2}=1.572...[/tex]

Would you (or Hurkyl or anyone else) tell me where my problem is?

Thanks,
Salty

Edit: corrected to reflect relation of even members in terms of R0