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May 10th, 2017, 07:57 AM  #1 
Senior Member Joined: Apr 2016 From: Australia Posts: 166 Thanks: 22 Math Focus: horses  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* Last edited by Adam Ledger; May 10th, 2017 at 08:23 AM. Reason: correction 
May 10th, 2017, 05:21 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,089 Thanks: 366 Math Focus: Yet to find out. 
Nice way to credit the founder.. Actually... is he even real.. i can't find anything on him xD.
Last edited by Joppy; May 10th, 2017 at 05:35 PM. 
May 10th, 2017, 08:46 PM  #3 
Senior Member Joined: Apr 2016 From: Australia Posts: 166 Thanks: 22 Math Focus: horses 
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. 
May 10th, 2017, 09:14 PM  #4 
Senior Member Joined: Apr 2016 From: Australia Posts: 166 Thanks: 22 Math Focus: horses  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.

May 10th, 2017, 09:58 PM  #5 
Senior Member Joined: Sep 2015 From: CA Posts: 1,202 Thanks: 613  
May 19th, 2017, 02:17 AM  #6 
Senior Member Joined: Apr 2016 From: Australia Posts: 166 Thanks: 22 Math Focus: horses 
seems a tad strange yes if I don't say so neil

May 19th, 2017, 02:24 AM  #7 
Senior Member Joined: Apr 2016 From: Australia Posts: 166 Thanks: 22 Math Focus: horses  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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