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