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November 20th, 2009, 08:23 AM   #1
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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 non-negative 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 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.
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November 20th, 2009, 09:39 AM   #2
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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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