[seqfan] Re: A033791

Andrew N W Hone A.N.W.Hone at kent.ac.uk
Wed Oct 15 18:32:37 CEST 2014


Hi David, 

I am not looking at the sequence just now but I guess theta_2 is a theta function in Jacobi's classical notation: see 

http://en.wikipedia.org/wiki/Theta_function

under "auxiliary functions". In the combinatorial setting, counting partitions, you want to set the first argument z=0, which gives the q-series 

\sum q^{(n+1/2)^2} 

where the sum is from n=-infinity to +infinity.

A good classical reference is A Course of Modern Analysis by Whittaker & Watson. The first volume of Mumford's Tata Lectures on Theta is also great, and has a more modern point of view. 

All the best,
Andy 
 
________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of David Newman [davidsnewman at gmail.com]
Sent: 15 October 2014 17:23
To: Sequence Fanatics Discussion list
Subject: [seqfan] A033791

I have a partition type sequence which matches A033791 for the first 40
terms.  However, beyond the computational evidence I have no reason to
think that the two are the same.  In fact, I'm guessing that they differ
for n>63.  I am hampered in my efforts  in part because I don't know which
function is meant by theta2.  Could someone give me the definition of
theta2 or point me to a source for the definition?

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