In a table of properly rounded function values, even and odd last decimals should appear about equally often. Test this for the 90 values of J₁(x) in Table A1 in App. 5.

Table A1

For more extensive tables see Ref. [GenRefl] in App. 1. x Jo(x) Jo(x) (4) 0.0 1.0000 -0.2601 0.3391 0.1 0.9975 -0.2921 0.3009 0.2 0.9900 -0.3202 0.2613 0.3 0.9776 -0.3443 0.2207 0.4 0.9604 -0.3643 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 201222324 56829 0.7652 0.7196 0.6711 0.6201 0.5669 0.9385 0.2423 3.5 0.9120 0.2867 3.6 0.8812 0.3290 3.7 0.8463 0.3688 3.8 0.8075 0.4059 3.9 0.5118 0.4554 0.3980 0.3400 0.2818 0.2239 0.1666 0.1104 0.0555 0.0025 2.5 -0.0484 ( 0.0000 0.0499 0.0995 0.1483 0.1960 2.6 -0.0968 2.7 -0.1424 2.8 -0.1850 2.9 -0.2243 0.4401 0.4709 X 3.0 3.1 3.2 3.3 3.4 4.0 -0.3971 4.1 -0.3887 0.4983 4.2 -0.3766 0.5220 4.3 -0.3610 0.5419 4.4 -0.3423 0.5767 0.5683 0.5560 0.5399 0.5202 0.5579 4.5 -0.3205 0.5699 4.6 -0.2961 0.5778 4.7 -0.2693 0.5815 4.8 -0.2404 0.5812 4.9 -0.2097 -0.3801 -0.3918 -0.3992 -0.4026 -0.4018 5.0 5.1 5.2 5.3 5.4 0.4416 5.7 0.4097 5.8 0.3754 5.9 0.4971 5.5 -0.0068 0.4708 5.6 0.0270 0.0599 0.0917 0.1220 6.0 6.1 6.2 6.3 0.1792 6.4 0.1374 6.5 0.0955 6.6 0.0538 6.7 0.0128 6.8 -0.0272 -0.0660 -0.1033 -0.1386 -0.1719 -0.2028 -0.2311 -0.2566 -0.2791 -0.2985 -0.3147 -0.1776 -0.1443 -0.3371 -0.1103 -0.0758 -0.0412 -0.3276 -0.3432 -0.3460 X -0.3453 -0.3414 -0.3343 6.9 70 71 72 73 74 75 76 7 78 79 80 81 82 88 84 7.7 8.3 8.5 8.6 -0.3241 8.7 -0.3110 -0.2951 (x) 0.1506 0.1773 0.2017 0.2238 0.2433 0.2601 0.2740 0.2851 0.2931 0.2981 0.3001 0.2991 0.2951 0.2882 0.2786 0.2663 0.2516 0.2346 0.2154 0.1944 0.1717 0.1475 0.1222 0.0960 0.0692 0.0419 0.0146 -0.0125 8.8 -0.0392 8.9 -0.0653 (t) -0.2767 -0.2559 -0.2329 -0.2081 -0.1816 -0.1538 -0.1250 -0.0953 -0.0652 -0.0349 -0.0047 0.0252 0.0543 0.0826 0.1096 0.1352 0.1592 0.1813 0.2014 0.2192 0.2346 0.2476 0.2580 0.2657 0.2708 0.2731 0.2728 0.2697 0.2641 0.2559 Jo(x) = 0 for x = 2.40483, 5.52008, 8.65373, 11.7915, 14.9309, 18.0711, 21.2116, 24.3525, 27.4935, 30.6346 J(x) = 0 for x = 3.83171, 7.01559, 10.1735, 13.3237, 16.4706, 19.6159, 22.7601, 25.9037, 29.0468, 32.1897