brackets for roots of bessj0:
                lower      upper         f(lower)   f(upper)
  root   1      1.9800     2.4700         0.2354    -0.0334
  root   2      5.4100     5.9000        -0.0378     0.1220
  root   3      8.3500     8.8400         0.0826    -0.0497
  root   4     11.7800    12.2700        -0.0027     0.1049
  root   5     14.7200    15.2100         0.0436    -0.0564
  root   6     17.6600    18.1500        -0.0759     0.0148
  root   7     21.0900    21.5800         0.0211    -0.0619
  root   8     24.0300    24.5200        -0.0516     0.0269
  root   9     27.4600    27.9500         0.0051    -0.0665
  root  10     30.4000    30.8900        -0.0336     0.0363
  root  11     33.3400    33.8300         0.0583    -0.0074
  root  12     36.7700    37.2600        -0.0193     0.0440
  root  13     39.7100    40.2000         0.0432    -0.0178
  root  14     43.1400    43.6300        -0.0073     0.0504
  root  15     46.0800    46.5700         0.0303    -0.0265
  root  16     49.0200    49.5100        -0.0509     0.0031