For brevity, we denote the reciprocal function as below begin{aligned} rho (s)equiv {mathbf frac} Big (frac{1}{eta (s)}Big )=frac{1}{eta (s)}-1.
The 400-m run time data were skewed and successfully normalized before analysis with the reciprocal function (i.e., transformed value = 1/original value).
end{aligned} (21)Now that what we concerned most is the values of the Riemann zeta function at integers for the moment, the asymptotic behavior of the ratio of the reciprocal function (21) at odd integers and even integers interests us.
For the benefit of accuracy, we regard the geometric mean values of (28a) and (b) as the approximate values of the reciprocal function (rho (2n+1)), namely begin{aligned} rho (2n+1){approx }sqrt{rho (2n rho (2n+2)} end{aligned} (32 which is the most valuable ingredient of our algorithm.
At each SOA, the regression equation of the reciprocal function relating the estimated DL (DLest).
We are well aware this could be a criticism to our model, although experimentally we chose a realistic domain for the reciprocal function.
All of these r s were smaller; thus, the reciprocal function appears to explain the variance of diminishing returns best.
At each SOA, we fitted the reciprocal function through the DLs at 1, 2, 4, and 6 intervals, and Table 3 gives the reciprocal regression equations and, as the coefficients of determination (r's) show, the reciprocal functions describe the data of Drake and Botte very well at almost all SOAs.
Note the 1/x mi/l represents the reciprocal function.
The first is the inverse trig function, meaning that if you put in the value of a ratio, it will give you the corresponding angle, the second is the reciprocal function meaning the ratio is reversed.
