k(beta_k-1) at k = 100,150,200,250,260,270,279,280: ['0.146664', '0.142015', '0.14035', '0.138668', '0.138425', '0.138233', '0.138088', '0.138075']
differences y_k - y_{k-1} for k = 271..280: ['-2.1e-5', '-1.6e-5', '-1.31e-5', '-1.63e-5', '-1.93e-5', '-1.46e-5', '-1.17e-5', '-1.48e-5', '-1.78e-5', '-1.33e-5']
fit a + b/k                      coefficients ['0.133619', '1.2949']   max residual 0.000359
fit a + b/sqrt(k)                coefficients ['0.127022', '0.185807']   max residual 0.000226
fit a + b/log(k)                 coefficients ['0.105332', '0.184618']   max residual 0.000199
fit a + b/sqrt(k) + c/k          coefficients ['0.114429', '0.542553', '-2.50111']   max residual 0.000155
nice -n 10 venv/bin/python beta_fit.py  24.05s user 0.12s system 99% cpu 24.199 total
