exact Jacobi parameters beta_1..beta_153 from m_0..m_306; algorithms (i) and (ii) agree on beta_1..beta_153: True
beta_1..beta_8 = 4, 2, 4/3, 7/6, 11/10, 414/385, 16868/15939, 102259729/97766928
all beta_k > 0: True
k:                   10         20         50        100        120        140        150        153
beta_k:        1.030482   1.010177  1.0031056  1.0014666  1.0012009  1.0010179  1.0009468  1.0009274
k(beta_k-1):     0.3048     0.2035     0.1553     0.1467     0.1441     0.1425      0.142     0.1419
k^2(beta_k-1-0.14/k) and other fits are not attempted here.
K = 100: Gauss nodes of mu above 1.99 (node / weight):
    2.5858266060482044486315152361168 / 0.2513316546384193145305057
    2.0114856925967879443266567831671 / 0.003128510323742977317009152
    2.0014629834706759675756532645008 / 0.000313649732097475144922795
    1.9973936523666215273657431135219 / 0.0005097752771099466696198457
    1.9909541084289203068433624175699 / 0.0007389478503046999311569223
    total Gauss weight of the nodes in [-2,2]: 0.49045237   (2 * sum of weights above 2 = 0.50954763)
    compression nu (K-1 = 99 levels): node above 2.05: 2.101990760466021919875227 / weight 0.0998095879805496
    density estimate at x = 0, 0.5, 1.0, 1.41, 1.5, 1.75, 1.9, 1.97: 0.1319, 0.12966, 0.12546, 0.12073, 0.11934, 0.10988, 0.10113, 0.094853
K = 125: Gauss nodes of mu above 1.99 (node / weight):
    2.5858266060482044486315152361168 / 0.2513316546384193145305057
    2.0114856946448637534884926670483 / 0.003128504582085395475554013
    2.0016838983724871079036770861703 / 0.0002388896036351059399980946
    1.9991501659390814440150165640517 / 0.0003047444865514847276065268
    1.9952193061871281720088949671454 / 0.0004560695505264409076741198
    total Gauss weight of the nodes in [-2,2]: 0.4906019   (2 * sum of weights above 2 = 0.5093981)
    compression nu (K-1 = 124 levels): node above 2.05: 2.101990760466021919875227 / weight 0.0998095879805496
    density estimate at x = 0, 0.5, 1.0, 1.41, 1.5, 1.75, 1.9, 1.97: 0.13207, 0.1298, 0.12531, 0.1205, 0.1193, 0.10993, 0.10088, 0.098848
K = 153: Gauss nodes of mu above 1.99 (node / weight):
    2.5858266060482044486315152361168 / 0.2513316546384193145305057
    2.0114856946581160855020319239067 / 0.003128504534644971578587724
    2.0017443668891603994597667708978 / 0.0002115366610407002019382518
    1.9999838909872360581708342218611 / 0.0001894412805384879381368389
    1.9974912318281990306957471420653 / 0.0002921916321543349001961179
    1.9939887548512329405550778090807 / 0.0003878709726245849797912866
    total Gauss weight of the nodes in [-2,2]: 0.49065661   (2 * sum of weights above 2 = 0.50934339)
    compression nu (K-1 = 152 levels): node above 2.05: 2.101990760466021919875227 / weight 0.0998095879805496
    density estimate at x = 0, 0.5, 1.0, 1.41, 1.5, 1.75, 1.9, 1.97: 0.13206, 0.12978, 0.12545, 0.12052, 0.11913, 0.11042, 0.10137, 0.095593
