Environmental Engineering Reference
In-Depth Information
D.2.2.5 Tabulated Values of Useful Bessel Functions
TABLE D.2. Useful Bessel Functions
x
I
0
(
x
)
K
0
(
x
)
I
1
(
x
)
K
1
(
x
)
K
1
(
x
)
x
I
0
(
x
)
K
0
(
x
)
I
1
(
x
)
K
1
(
x
)
.420
1.0446
1.0721
.2147
2.0590
.001
1.0000
7.0237
.0005
999.9962
.430
1.0468
1.0518
.2200
2.0006
.002
1.0000
6.3305
.0010
499.9932
.440
1.0490
1.0321
.2254
1.9449
.003
1.0000
5.9251
.0015
333.3237
.450
1.0513
1.0129
.2307
1.8915
.004
1.0000
5.6374
.0020
249.9877
.460
1.0536
.9943
.2361
1.8405
.005
1.0000
5.4143
.0025
199.9852
.470
1.0560
.9761
.2415
1.7916
.006
1.0000
5.2320
.0030
166.6495
.480
1.0584
.9584
.2470
1.7447
.007
1.0000
5.0779
.0035
142.8376
.490
1.0609
.9412
.2524
1.6997
.008
1.0000
4.9443
.0040
124.9782
.500
1.0635
.9244
.2579
1.6564
.009
1.0000
4.8266
.0045
111.0871
.510
1.0661
.9081
.2634
1.6149
.010
1.0000
4.7212
.0050
99.9739
.520
1.0688
.8921
.2689
1.5749
.020
1.0001
4.0285
.0100
49.9547
.530
1.0715
.8766
.2744
1.5364
.030
1.0002
3.6235
.0150
33.2715
.540
1.0742
.8614
.2800
1.4994
.040
1.0004
3.3365
.0200
24.9233
.550
1.0771
.8466
.2855
1.4637
.050
1.0006
3.1142
.0250
19.9097
.560
1.0800
.8321
.2911
1.4292
.060
1.0009
2.9329
.0300
16.5637
.570
1.0829
.8180
.2967
1.3960
.070
1.0012
2.7798
.0350
14.1710
.580
1.0859
.8042
.3024
1.3638
.080
1.0016
2.6475
.0400
12.3742
.590
1.0889
.7907
.3080
1.3328
.090
1.0020
2.5310
.0450
10.9749
.600
1.0920
.7775
.3137
1.3028
.100
1.0025
2.4271
.0501
9.8538
.610
1.0952
.7646
.3194
1.2738
.110
1.0030
2.3333
.0551
8.9353
.620
1.0984
.7520
.3251
1.2458
.120
1.0036
2.2479
.0601
8.1688
.630
1.1017
.7397
.3309
1.2186
.130
1.0042
2.1695
.0651
7.5192
.640
1.1051
.7277
.3367
1.1923
.140
1.0049
2.0972
.0702
6.9615
.650
1.1084
.7159
.3425
1.1668
.150
1.0056
2.0300
.0752
6.4775
.660
1.1119
.7043
.3483
1.1420
.160
1.0064
1.9674
.0803
6.0533
.670
1.1154
.6930
.3542
1.1181
.170
1.0072
1.9088
.0853
5.6784
.680
1.1190
.6820
.3600
1.0948
.180
1.0081
1.8537
.0904
5.3447
.690
1.1226
.6711
.3659
1.0722
.190
1.0090
1.8018
.0954
5.0456
.700
1.1263
.6605
.3719
1.0503
.200
1.0100
1.7527
.1005
4.7760
.710
1.1301
.6501
.3778
1.0290
.210
1.0111
1.7062
.1056
4.5317
.720
1.1339
.6399
.3838
1.0083
.220
1.0121
1.6620
.1107
4.3092
.730
1.1377
.6300
.3899
.9882
.230
1.0133
1.6199
.1158
4.1058
.740
1.1417
.6202
.3959
.9686
.240
1.0145
1.5798
.1209
3.9191
.750
1.1456
.6106
.4020
.9496
.250
1.0157
1.5415
.1260
3.7470
.760
1.1497
.6012
.4081
.9311
.260
1.0170
1.5048
.1311
3.5880
.770
1.1538
.5920
.4142
.9130
.270
1.0183
1.4697
.1362
3.4405
.780
1.1580
.5829
.4204
.8955
.280
1.0197
1.4360
.1414
3.3033
.790
1.1622
.5740
.4266
.8784
.290
1.0211
1.4036
.1465
3.1755
.800
1.1665
.5653
.4329
.8618
.300
1.0226
1.3725
.1517
3.0560
.810
1.1709
.5568
.4391
.8456
.310
1.0242
1.3425
.1569
2.9441
.820
1.1753
.5484
.4454
.8298
.320
1.0258
1.3136
.1621
2.8390
.830
1.1798
.5402
.4518
.8144
.330
1.0274
1.2857
.1673
2.7402
.840
1.1843
.5321
.4581
.7993
.340
1.0291
1.2587
.1725
2.6470
.850
1.1889
.5242
.4646
.7847
.350
1.0309
1.2327
.1777
2.5591
.860
1.1936
.5165
.4710
.7704
.360
1.0327
1.2075
.1829
2.4760
.870
1.1984
.5088
.4775
.7564
.370
1.0345
1.1832
.1882
2.3973
.880
1.2032
.5013
.4840
.7428
.380
1.0364
1.1596
.1935
2.3227
.890
1.2080
.4940
.4905
.7295
.390
1.0384
1.1367
.1987
2.2518
.900
1.2130
.4867
.4971
.7165
.400
1.0404
1.1145
.2040
2.1844
.910
1.2180
.4796
.5038
.7039
.410
1.0425
1.0930
.2093
2.1202
Continued
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