Page 173 - Essentials of applied mathematics for scientists and engineers

book Mobk070 March 22, 2007 11:7

APPENDIX A: THE ROOTS OF CERTAIN TRANSCENDENTAL EQUATIONS 163

TABLE A.3: The first six roots α n ,of
αJ 1 (α) − CJ 0 (α) = 0
C α 1 α 2 α 3 α 4 α 5 α 6
0 0 3.8317 7.0156 10.1735 13.3237 16.4706
0.01 0.1412 3.8343 7.0170 10.1745 13.3244 16.4712
0.02 0.1995 3.8369 7.0184 10.1754 13.3252 16.4718
0.04 0.2814 3.8421 7.0213 10.1774 13.3267 16.4731
0.06 0.3438 3.8473 7.0241 10.1794 13.3282 16.4743
0.08 0.3960 3.8525 7.0270 10.1813 13.3297 16.4755
0.1 0.4417 3.8577 7.0298 10.1833 13.3312 16.4767
0.15 0.5376 3.8706 7.0369 10.1882 13.3349 16.4797
0.2 0.6170 3.8835 7.0440 10.1931 13.3387 16.4828
0.3 0 7465 3.9091 7.0582 10.2029 13.3462 16.4888
0.4 0.8516 3.9344 7.0723 10.2127 13.3537 16.4949
0.5 0.9408 3.9594 7.0864 10.2225 13.3611 16.5010
0.6 1.0184 3.9841 7.1004 10.2322 13.3686 16.5070
0.7 1.0873 4.0085 7.1143 10.2419 13.3761 16.5131
0.8 1.1490 4.0325 7.1282 10.2516 13.3835 16.5191
0.9 1.2048 4.0562 7.1421 10.2613 13.3910 16.5251
1.0 1.2558 4.0795 7.1558 10.2710 13.3984 16.5312
1.5 1.4569 4.1902 7.2233 10.3188 13.4353 16.5612
2.0 1.5994 4.2910 7.2884 10.3658 13.4719 16.5910
3.0 1.7887 4.4634 7.4103 10.4566 13.5434 16.6499
4.0 1.9081 4.6018 7.5201 10.5423 13.6125 16.7073
5.0 1.9898 4.7131 7.6177 10.6223 13.6786 16.7630
6.0 2.0490 4.8033 7.7039 10.6964 13.7414 16.8168
7.0 2.0937 4.8772 7.7797 10.7646 13.8008 16.8684
8.0 2.1286 4.9384 7.8464 10.8271 13.8566 16.9179
9.0 2.1566 4.9897 7.9051 10.8842 13.9090 16.9650
10.0 2.1795 5.0332 7.9569 10.9363 13.9580 17.0099
15.0 2.2509 5.1773 8.1422 11.1367 14.1576 17.2008
20.0 2.2880 5.2568 8.2534 11.2677 14.2983 17.3442
30.0 2.3261 5.3410 8.3771 11.4221 14.4748 17.5348
40.0 2.3455 5.3846 8.4432 11.5081 14.5774 17.6508
50.0 2.3572 5.4112 8.4840 11.5621 14.6433 17.7272
60.0 2.3651 5.4291 8.5116 11.5990 14.6889 17.7807
80.0 2.3750 5.4516 8.5466 11.6461 14.7475 17.8502
100.0 2.3809 5.4652 8.5678 11.6747 14.7834 17.8931
∞ 2.4048 5.5201 8.6537 11.7915 14.9309 18.0711