[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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