Re: Question on finding eta expansions

["LNU, Swati" <S10@email.sc.edu>]

Yes, this is what I had in my mind too. It was mentioned in a paper so I thought something is off. Thanks for the clarification. 

Swati

"The pursuit of science is at its best when it is a part of a way of life" - Alladi Ramakrishnan.

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From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>
Sent: Friday, September 13, 2024 5:06 PM
To: pari-users@pari.math.u-bordeaux.fr <pari-users@pari.math.u-bordeaux.fr>
Subject: Re: Question on finding eta expansions

 

On Fri, Sep 13, 2024 at 08:28:42PM +0000, LNU, Swati wrote:
> Dear Professor,
> Thank you for your reply. I have a follow-up question:
> The first few terms of series expansion of (eta(2z)^3 *  eta(3z)^2 *  eta(12z)^2) / (eta(6z)^2) = q - 3q^3 - q^4 + 6q^6 + 6q^7 - 3q^9 + ...
> On writing the code:
> D(n) = {q * eta(q^(24 * 2) + O(q^(24 * ( n + 1))))^(3) * eta(q^(24 * 3) + O(q^(24 * (n + 1))))^(2) * eta(q^(24 * 12) + O(q^(24 * (n + 1))))^(2) * eta(q^(24 * 6) + O(q^(24 * (n + 1))))^(-2);}

This is not correct, the first term should be q^((2*3+3*2+12*2-6*2)) = q^24, not q.

Cheers,
Bill