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 and a starting value 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 nonnegative values) in which I'm asked to define to which values it will be a convergent series, and from those values to calculate its limits. Usually in nongeneralized 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 doublyexponential. 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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