(EDIT: Powers of $q$ in the formula corrected.)


I've been doing some computations with skein modules, and I found the following formula for the N-th colored Jones polynomial of the trefoil:


$\frac{1}{q^2-q^6}\sum\_{i=1}^{N+1} (-1)^i q^{6(N^2-i^2)}(q^{10i-4}-q^{2i})$


I'm interested in comparing this to formulas that appear in the literature. I'm pretty sure I've seen similar formulas before, but I haven't been able to find them again.



> 
> Where can I find explicit formulas for colored Jones polynomials of the trefoil (or even better, for some family of "small" knots that includes the trefoil)?
> 
> 
> 


(To be precise I'll explain my normalization. Identify the Kauffman bracket skein module of the tubular neighborhood of the (0-framed) trefoil with $\mathbb C[x]$, where $x^n$ is identified with $n$ parallel copies of the trefoil. When I say "N-th colored Jones polynomial," I mean the Chebyshev polynomial $S\_N(x)$ viewed as an element of the skein module of $S^3$. In particular, the first Jones polynomial of the unknot is $-q^2-q^{-2}$.) (Again, to be precise, $S\_0=1, S\_1=x$, and $S\_{n+1}(x) = xS\_n(x) - S\_n(x)$.)



Closed formula for colored Jones polynomial of the trefoil? (reference request)
This appears to be done by K. Habiro in ["On the colored jones polynomials of some simple links"](http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1172-3.pdf) (the trefoil is the last section of the paper).


