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May 10th, 2017, 08:57 AM  #1 
Senior Member Joined: Apr 2016 From: Australia Posts: 177 Thanks: 22 Math Focus: horses,cash me outside how bow dah, trash doves  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 09:23 AM. Reason: correction 
May 10th, 2017, 06:21 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,461 Thanks: 489 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 06:35 PM. 
May 10th, 2017, 09:46 PM  #3 
Senior Member Joined: Apr 2016 From: Australia Posts: 177 Thanks: 22 Math Focus: horses,cash me outside how bow dah, trash doves 
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, 10:14 PM  #4 
Senior Member Joined: Apr 2016 From: Australia Posts: 177 Thanks: 22 Math Focus: horses,cash me outside how bow dah, trash doves  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, 10:58 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 1,660 Thanks: 844  
May 19th, 2017, 03:17 AM  #6 
Senior Member Joined: Apr 2016 From: Australia Posts: 177 Thanks: 22 Math Focus: horses,cash me outside how bow dah, trash doves 
seems a tad strange yes if I don't say so neil

May 19th, 2017, 03:24 AM  #7 
Senior Member Joined: Apr 2016 From: Australia Posts: 177 Thanks: 22 Math Focus: horses,cash me outside how bow dah, trash doves  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

June 13th, 2017, 10:46 AM  #8 
Senior Member Joined: Apr 2016 From: Australia Posts: 177 Thanks: 22 Math Focus: horses,cash me outside how bow dah, trash doves 
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
Last edited by Adam Ledger; June 13th, 2017 at 10:50 AM. 
June 13th, 2017, 11:04 AM  #9 
Senior Member Joined: Apr 2016 From: Australia Posts: 177 Thanks: 22 Math Focus: horses,cash me outside how bow dah, trash doves 
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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