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Quintuple Product Identity

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Moderator: Shobhit

Post Sun Sep 08, 2013 8:33 am
Shobhit Site Admin
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Posts: 852
Location: Jaipur, India

Prove that

\(\displaystyle \prod_{n=1}^\infty \left( 1-q^n\right)\left(1-z q^n \right)\left( 1-z^{-1}q^{n-1}\right)\left( 1-z^2 q^{2n-1}\right)\left( 1-z^{-2}q^{2n-1}\right)=\sum_{m=-\infty}^{\infty} \left(z^{3m}-z^{-3m-1} \right)q^{m(3m+1)/2}\)

Post Tue Sep 10, 2013 5:21 pm

Posts: 138
Location: North Londinium, UK
Way beyond me, but I look forward the proof... :shock:

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