The QRS constant, denoted 
(OEIS A131329), is the unique root
of 
in the open
interval 
,
where 
is the Hurwitz zeta function (Bailey et
al. 2009). It arises in a class of 
coupled oscillators studied by Quinn et al. (2007),
whose bifurcation phase offset has asymptotic behavior 
.
A related constant conjectured by Quinn et al. (2007) to exist was defined in terms of the sum
![S(N,a)=sum_(i=1)^N[1-a^2(1-(2i-2)/(N-1))^2]^(-3/2)](/images/equations/QRSConstant/NumberedEquation1.svg) |
(1)
|
for an integer 
and 
, and given by
 |
(2)
|
(OEIS A131330). Bailey et al. (2009) gave a sketch of a proof of the exact value
 |
(3)
|
