Let $a(q)$ denote the Borwein function $$a(q)=\sum_{m,n=-\infty}^\infty q^{n^2+nm+m^2}.$$ In this research paper the author has obtained the series expansion for $a(q)a(q^4)$. I want the series expansion of $a^2(q)a^2(q^4)$. I have squared the series and obtained an expression, but that series seems to be very long and not expressible in powers of $q$. But I want a series representation in powers of $q$.

This is in reference to my M.Sc project and I need some guidance at the moment. Kindly help me out or at least point me in the right direction. At present I am not sure how to proceed.

obviouslya power series in q. Also, where exactly in the linked PDF is the series you refer to located? $\endgroup$ – Somos Mar 30 at 21:552more comments