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

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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