# [seqfan] Re: A033791

David Newman davidsnewman at gmail.com
Wed Oct 15 23:51:46 CEST 2014

The sequence that I'm working with will agree with A033791 for n<64, but
will be different thereafter.  Should I propose it as new sequence or as a
comment on A033791.

On Wed, Oct 15, 2014 at 12:32 PM, Andrew N W Hone <A.N.W.Hone at kent.ac.uk>
wrote:

> 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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