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July 7th, 2012, 12:09 PM   #1
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Functional equation with a recurrence relation.

I rarely post on this section but this time I've got a real problem.

Consider the recurrence function:



My goal is to find the functional form of L(n).

From examining the first 17 outputs, I conclude that this function is related to logarithmic function.

Thank you all.
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July 7th, 2012, 02:53 PM   #2
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You need to revise the definition so that it doesn't imply L(0) = L(0) + 1, which is impossible.
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July 7th, 2012, 11:43 PM   #3
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reply to skipjack

Quote:
Originally Posted by skipjack
You need to revise the definition so that it doesn't imply L(0) = L(0) + 1, which is impossible.
L(0) is undefiend.

With the use of advanced GDC, theory of curve fitting and purely iterative algorithms, I found:


But cannot prove it without iteration.

Any help is appritiated.
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