Справочник по специальным функциям - Абрамович М.
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1 0. 0.4788 0.9054 1.232 1.417 1.435 1.276 0.9562 0.5119 0
2 0 0.3896 0.7509 1.052 1.253 1.316 1.212 0.9335 0.5088 0
3 0 0.2780 0.5538 0.8148 1.030 1.149 1.118 0.0992 0.5039 0
4 0 0.1762 0.3683 0.5813 0.7968 0.9643 1.008 0.8575 0.4979 0
5 0 0.1011 0.2254 0.3896 0.5906 0.7879 0.8957 0.8127 0.4911 0
1 0 0.9928 1.745 2.075 1.903 1.280 0.3775 -0.5521 -1.244 -1.500
2 0 0.9559 1.710 2.092 1.998 1.432 0.5298 -0.4541 -1.214 -1.500
3 0 0.В745 1.611 2.063 2.097 1.640 0.7606 -0.2972 -1.174 -1.500
4 0 0.7393 1.418 1.934 2.128 1.841 1.032 -0.0951 -1.097 -1.500
5 0 0.5662 1.146 1.691 2.047 1.975 1.299 +0.1319 -1.017 -1.500
1 0 0.0844 0.3295 0.7111 1.1B9 1.710 2.211 2.627 2.903 3.000
2 0 0.0690 0.2744 0.6092 1.054 1.572 2.101 2.566 2.886 3.000
3 0 0.0500 0.2051 0.4773 0.8738 1.380 1.944 2.475 2.859 3.000
4 0 0.0328 0.1405 0.3487 0.6876 1.171 1.764 2.367 2.827 3.000
S 0 0.0198 0.0898 0.2414 0.5212 0.9701 1.580 2.251 2.791 3,000
1 0 0.4222 1.570 3.116 4.596 5.530 5.548 4.501 2.522 0
2 0 0.3597 1.358 2.755 4.175 5.170 5.327 4.417 2.510 0
3 0 0.2765 1.070 2.255 3.576 4.641 4.994 4.286 2.491 0
4 0 0.1934 0.7758 1.723 2.909 4.025 4.583 4.122 2.466 а
5 0 0.1244 0.5226 1.243 2.269 3.395 4.150 3.936 2.437 0
Взято из [21,4]. 574
21. СФЕРОИДАЛЬНЫЕ ВОЛНОВЫЕ ФУНКЦИИ
Таблица 21.2. Угловые функции — вытянутые и сплюснутые
Сплюснутые S™(-io, ч)
1.00 IT 1.000 1.000 1.000 1.000
о о о о о
-0,5000 -0.5000 -0.5000 -0,5000 -0.5000
0.1 1.002 1.008 1.022 1.017 1.083
0.1001 0.1004 0.1011 0.1016 0.1032
-0.4863 -0.4897 -0.4943 -0.4994 -0.5061
0.2 1.007 1.032 1.089 !.191 1.341
0.2009 0.2034 0.2079 0.2150 0.2252
-0. 4450 -0.4585 -0. 4766 -0. 4966 -0. 5234
0.3 1.01 S 1.073 1.205 1.449 1.835
0.302? 0.3114 0.3273 0.3526 0.3884
-0.3757 -0.4052 -0.4448 -0.4891 -0.5495
0.4
1.028 1.132
1.377 1.854 2.648
0.4065 0.4274 D.4664 0.5298 0.6252
-0.2779 -0.3277 -0.3952 -0.4716 -0.5780
0.5
1.044 1.210 1.617 2.452 3.952
0.5128 0.5542 0.6338 0.7681 0,9804
-0.1507 -0.2231 -0.3223 -0.4356 -0.5977
0.6 1.064 1.310 1.940 3.319 6.000
0.6222
0.6952 0.8398 1.096 ¦1.525
+0.0070 -0.0872 -0.2183 -0.3681 -0.5869
0 3 1 0 -0.1477 -0.2810 -0.3855 -0.4466 -0.4491 -0.3768
0 -0.1480 -0.2839 -0.3947 -0.4668 -0.4839 -0.4275
3 0 -0.1486 -0.2885 -0.4097 -0.4998 -0.5421 -0.5140
4 0 -0.1495 -0.2949 -0.4306 -0.5415 -0.6270 -0.6432
0 -0.1504 -0.3033 -0.4589 -0.6123 -0.7489 -0.8356
1 1 1 1.000 0.9961 0.9838 0.9628 0.9316 0.8884 0.8299
1.000 0.9994 0.9973 0.9923 0.9827 0.9652 0.9340
1.000 1.006 1.025 1.055 1,093 1.135 1.172
4 1.000 1.020 1.079 1.178 1.319 1.498 1,708
1.000 1.041 1.174 1.406 1.776 2.242 2.878
1 2 1 0 0.2987 0.5897 0.8643 1.113 1.322 1.478
0 0.2985 0.5950 0.8815 1.153 1.398 1.600
0 0. 3005 0.6043 0.9140 1,228 1.541 1.837
4 0 0.3022 0.6213 0.9640 1.349 1.780 2.250
0 0. 2990 0.6400 1.040 1.537 2.165 2.947
I 3 1 -1.500 -1.421 -1.169 -0.8136 -0.3165 0.2710 0.9015
-1.500 -1.431 -1.228 -0.8941 -0.4427 + 0.1060 0.7174
3 -1.500 -1.447 -1.289 -1.024 -0.6502 -0.1738 + 0.3916
4 -1.500 -1.467 -1.364 -1.184 -0.9148 -0.5415 -0.0538
-1.500 -1.486 -1.442 -1.353 -1.198 -0.9435 -0.5506
2 2* 1 3.000 2.972 2.889 2.748 2.549 2.291 1.970
3.000 2.979 2.915 2.805 2.644 2.425 2.138
3 3.000 2.992 2.965 2.915 2.830 2.693 2.481
3.000 3.013 3.052 3.111 3.170 3.200 3.157
3.000 3.052 3.211 3.469 3.813 4.202 4.564
2 3 1 0 1.486 2.886 4.115 5.086 5.704 5.877
0 1.488 2.906 4,1В0 5.226 5.954 6.251
3 0 1.494 2.943 4.295 5.482 6.413 6.951
4 0 1.498 2.996 4.475 5.891 7.166 8.132
5 Q 1.509 3.073 4,738 6.515 8.347 10.07
0.7 1.088 1.434 2.366 4.557 9.211
0.7353
0.8539
1.098
1.552
2.369
0.1965 + 0.0849 -0.0721 -0.2485 -0.5067
-0.2130 -0.2757 -0.3841 -0.5540 -0.8080
0.7506 0.8802 1.188 1.920 3.642
1.554 1.730 2.0R? 2.723 3.868
1.501 1.329 1.006 0.5403 0.0161
1.585 1.770 2.161 2.966 4.746
5.503 5.982 6.904 8.515 11.28
0.8 0.9 1.0
1.115 1.147 1.183
1.585 1.767 1.986
2.923 3.648 4.589
6.323 8.837 12.42
14.23 22.11 34.48
0.8530 0.9760 1.105
1.035 1.243 1.484
1.425 1.842 2.378
2.195 3.105 4.396
3.684 5.741 8.970
0.4197 0.6784 $.9749
0.2999 0.5660 0.8930
+0.1311 0.3845 0.7958
-0.0458 0.2868 0.8201
-0.2880 0.1892 1.132
+0.0600 0.4613 1.011
-0.0015 0.4274 1.051
-0.1091 0.3711 1.138
-0.2765 0.2912 1.327
-0.5447 0.1715 1.723
0.6402 0.4731 0
0.7864 0.6118 0
1.149 0.9724 0
2.067 1.950 0
4.400 4.651 0
1.508 1.247 0
1.734 1.487 0
2.200 2.000 0
3.092 3.033 0
4.786 5.138 0
1.946 1.988 0
1.826 1.951 0
1.572 1.834 0
1.177 1.619 0
0.7471 1.439 0
1.131 0.6041 0
1.305 0.7234 0
1.687 0.9944 о
2.512 1.615 0
4.460 3.188 0
4.477 2.683 0
4.990 3.077 0
6.008 3.879 0
7.857 5.408 0
11.21 8.354 0 ВЫТЯНУТЫЕ РАДИАЛЬНЫЕ ФУНКЦИИ 575
Таблица 21.3. Вытянутые радиальные функции первого и второго рода
(-1)3.153 (-1)5.289 (-1)6.064 (-1)5.892 (-1)5.381
(-2) 4.470 (-1)1.696 (-1) 3.295 (-1 4.507 (-1)4.952
