Quinn et al. (2007) investigated a class of 
coupled oscillators whose bifurcation phase offset had a conjectured
asymptotic behavior of 
,
with an experimental estimate for the constant 
as 
(OEIS A131329).
Rather amazingly, Bailey et al. (2007) were able to find a closed form for
as the unique root of 
in the interval ![[0,2]](/images/equations/QRSConstant/Inline7.svg)
, where 
is a Hurwitz zeta
function.
A related constant conjectured by Quinn et al. (2007) to exist was defined in terms of
![S(N,a)=sum_(i=1)^N[1-a^2(1-(2i-2)/(N-1))^2]^(-3/2)](/images/equations/QRSConstant/NumberedEquation1.svg) |
(1)
|
and given by
 |
(2)
|
(OEIS A131330). Even more amazingly, the exact value of this constant was also found by Bailey et al. (2007) without full proof, but with enough to indicate that such a proof could in principle be constructed, to have the exact value
![C=1/4zeta(3/2,1/2c_1)].](/images/equations/QRSConstant/NumberedEquation3.svg) |
(3)
|
