Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55)
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MISCELLANEOUS FUNCTIONS 1001 [27.5] National Bureau of Standards, Table of the Sievert [27.6] R. M. Sievert, Die v-Strahlungsintensitat an der integral, Applied Math. Series- (U.S. Government Oberflache und in der nachsten Umgebuns von Printing Office, Washington, D.C. I n press). Radiumnadeln, Acta Radiologica 11, 239-301 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0 1. 2 1. 4 1. 6 1. 8 2. 0 2. 2 2. 4 2. 6 2. 8 3. 0 3. 5 4. 0 4. 5 5. 0 5. 5 6. 0 6. 5 7. 0 7. 5 8. 0 8. 5 9. 0 9. 5 10. 0 ~=0(.01)2(.02)5(.05) 10, e=0°(10)900, 9D. loo 0. 174533 0. 157843 0. 142749 0. i29099 0. 116754 0. 105589 0. 095492 0. 086361 0. 078103 0.070634 0.063880 0. 052247 0. 042733 0. 034951 0.028587 0. 023381 0. 019123 0. 015641 0. 012793 0. 010463 0. 008558 0. 005178 0. 003132 0.001895 0.001147 0. 000694 0. 000420 0. 000254 0. 000154 0. 000093 0.000056 0.000034 ....-~ 0.000021 0.000012 0. 000008 Sievert Integral e-zsec 4 s o b & 20° 0.349066 0. 315187 0.284598 0. 256978 0. 232040 0. 209522 0. 189191 0. 170833 0. 154256 0. 139289 0. 125775 0. 102553 0. 083620 0.068183 0.055597 0.045335 0. 036967 0.030145 0. 024582 0. 020045 0.016347 0. 009817 0.005896 0.003542 0.002127 0.001278 0.000768 0. 000461 0. 000277 0. 000167 0.000100 0. O O O O ~ ~ O . . . . . . . . 0.000036 0.000022 0. 000013 30' 0. 523599 0.471456 0.424515 0. 382255 0.344209 0.309957 0. 279118 0. 251353 0. 226354 0. 203845 0. 183579 0. 148899 0. 120780 0. 097979 0.079488 0.064492 0. 052329 0. 042463 0. 034460 0. 027968 0. 022700 0. 013477 0. 008005 0.004756 0.002828 0. 001682 0.001001 0. 000596 0. 000355 0.000211 0.000126 0. 000075 0. 000045 0. 000027 0.000016 27.5. fm(z) = tme-rz-? d t and Lrn Related Integrals m=O, 1 , 2 . . . Differential Equations 27.5.1 27-52 f&=-fm-l (m=l, 2 , . . .) ZfC'- (m - 1 )fC +2fm= 0 Recurrence Relation 27-53 2fm=(m-l)fm-2+~jm-3 ( m 2 3 ) 40' 0. 698132 0.625886 0.561159 0. 503165 0. 451198 0. 404629 0.362893 0. 325486 0. 291957 0. 261901 0. 234956 0. 189138 0. 152298 0. 122667 0. 098829 0. 079644 0. 064201 0.051766 0. 041750 0.033680 0. 027177 0.015912 0.009330 0.005478 0. 003221 0.001896 0. 001117 0. 000659 0. 000389 0. 000230 0. 000136 0.000081 0. 000048 0. 000028 0. 000017 [ (-;) '1 (1930). s,' e-* sec+d+, +=3O0(lo)9O0, A=0(.01).5, 3D. 50' 0.872665 0. 777323 0. 692565 0. 617194 0. 550154 0.490508 0. 437428 0.390178 0. 348109 0.310642 0.277267 0. 221027 0. 176336 0. 140792 0. 112497 0. 089954 0. 071979 0. 057635 0.046179 0.037024 0.029702 0. 017164 0. 009951 0.005787 0.003374 0.001972 0. 001155 0.000678 0. 000399 0. 000235 0. 000139 0. 000082 0. 000048 0. 000029 0.000017 60° 1. 047198 0. 923778 0.815477 0. 720366 0. 636769 0. 563236 0.498504 0. 441478 0. 391204 0. 346851 0.307694 0. 242523 0. 191533 0. 151541 0. 120105 0. 095342 0.075797 0. 060342 0. 048100 0.038387 0. 030670 0.017576 0. 010128 0.005862 0. 003407 0.001986 0. 001162 0. 000681 0. 000400 0. 000235 0. 000139 0. 000082 0. 000048 0. 000029 0. 000017 [ (-y] 75O 1.308997 1. 123611 0. 968414 0. 837712 0. 727031 0. 632830 0. 552287 0.483134 0.423535 0. 371996 0. 327288 0. 254485 0. 198885 0. 156087 0. 122932 0.097108 0. 076905 0. 061040 0. 048541 0.038667 0.030848 0. 017634 0. 010147 0.005869 0. 003409 0.001987 . . . . -. - . 0. 001162 0. 000681 0.000400 0. 000235 0. 000139 0. 000082 0. 000048 0. 000029 0.000017 Table 27.4 goo 1.570796 1. 228632 1. 023680 0.868832 0. 745203 0. 643694 0. 558890 0. 487198 0. 426062 0.373579 0. 328286 0. 254889 0. 199051 0. 156156 0. 122961 0. 097121 0.0769 11 0.061043 0. 048542 0.038668 0. 030848 0.017634 0. 010147 0.005869 0. 003409 0.001987 0. 001162 0.000681 0.000400 0. 000235 0.000139 0.000082 0.000048 0. 000029 0.000017 Power Series Representations -2 b k - 2 - (3k2- 6k + 2) Uk -2Uk-2 a - k - k ( k - l ) (k--2) bk= k(k-l)(k-2) uo= a,= 0 az=-b, b,=--JiF 6 2 x 2 3 (1-7) bo= 1 (For y, see chapter 6.)