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 November 20th, 2009, 08:23 AM #1 Newbie   Joined: Nov 2009 Posts: 1 Thanks: 0 Generalizing a recursive series Hey there, This one's been bugging me for a while: When introduced to a recursive series $a_{n}$ and a starting value $a_{1}$ is given, I could successfully point out the limit (if there is one) of that series. But if I'm requested to analyze the following generalized series: (alpha, x are non-negative values) $a_{n+1}= a^{2}_{n} + \alpha$ in which I'm asked to define to which $x,\alpha$ values it will be a convergent series, and from those values to calculate its limits. Usually in non-generalized form I don't find much difficulties. But here I can't find a good starting point from which I can derive any conclusions. I'd appreciate any kind of help to sort this one out. Thanks in advance.
 November 20th, 2009, 09:39 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Generalizing a recursive series They will in general be doubly-exponential. See Aho and Sloane 1970, which Dr. Sloane has on his website: http://www.research.att.com/~njas/doc/doubly.html

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