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May 10th, 2017, 07:57 AM   #1
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help with determining a pair of sequences

Hi I have been working on this for a while and haven't quite figured out yet what the sequences n,m are and was hoping for some assistance if anyone has studied this one before.

*that was meant to be n,m are elements of Q rather than Z*
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Last edited by Adam Ledger; May 10th, 2017 at 08:23 AM. Reason: correction
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May 10th, 2017, 05:21 PM   #2
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Nice way to credit the founder.. Actually... is he even real.. i can't find anything on him xD.
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Last edited by Joppy; May 10th, 2017 at 05:35 PM.
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May 10th, 2017, 08:46 PM   #3
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All horseplay aside as a side remark all m are strictly integers, and n should really be denoted q to represent its membership to Q. It definitely has a simple expression for the kth term for n(j,k) the main issue with using the form I have chosen will be finding such an expression for the integer powers of each zeta(2j+1) cofactor in each of the P(N) summands.

But naturally I choose this form just out of the sheer curiosity of having noted the fact that the total number of summands turns out to be the number palindromic partitions of N. What I want to establish is whether this is a consequence of performing the asymptotic series expansion for any expression in general, or this fact is intimately connected to this particular complex function.

as per usual its given me more reading to do that id like. actually hate reading tbh.
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May 10th, 2017, 09:14 PM   #4
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typical evaluation (here N=20)

as attached another point of interest is that the final (or initial depends how we skin the cat really) summand in the series is always an element of Z.
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May 10th, 2017, 09:58 PM   #5
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Nice way to credit the founder.. Actually... is he even real.. i can't find anything on him xD.
seems a little unlikely the Online ... anything.. was founded in 1964
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May 19th, 2017, 02:17 AM   #6
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seems a tad strange yes if I don't say so neil
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May 19th, 2017, 02:24 AM   #7
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just further material for those sincerely interested

this a more appropriate selection of F(z) to show that the relationship to the number P(N) in the expression involving zeta is more related to the algebra of an asymptotic series expansion rather than the specific function itself I originally prescribed
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June 13th, 2017, 09:46 AM   #8
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another related figureAttachment 8931 the approximation sign can be replaced with an equality sign on the condition that only z values which are roots of the gamma function are specified as domain
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June 13th, 2017, 10:04 AM   #9
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so basically I look at this area of mathematics as a 2d color coded "spider web" map ( its just such a very simplifying format for getting a grasp of a functional relationship involving this number of elementary functions), and ive placed the above approximation somewhat centrally.
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