Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55)
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27. Miscellaneous Functions 1 (14<2r,n21) (For Bernoulli numbers .&, see chapter 23.) 27.1. Debye Functions Series Representations 27.1.1 [27.1] J. A. Beattie, Six-place tables of the Debye energy and specific heat functions, J. Math. Phys. 6, $l'gls [l e ~ - e q l l l ' 2=0(.01)24, 6s. 1-32 (1926). yJdy 12 yJdy 32 I Relation to Riemann Zeta Function (see chapter 23) m 27.1.3 27.1.2 I [27.2] E. Gruneisen, Die Abhangigkeit des elektrischen + . . . +&I(s>O,nll) Table 27.1 X 0. 0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8 0. 9 1. 0 1. 1 1. 2 1. 3 1. 4 1. 6 1. 8 2. 0 2. 2 2. 4 2. 6 2. 8 3. 0 3. 2 3. 4 3. 6 3. 8 4. 0 4. 2 4. 4 4. 6 4. 8 5. 0 5. 5 6. 0 6. 5 7. 0 7. 5 8. 0 8. 5 9. 0 9. 5 10. 0 1.000000 0.975278 0. 951111 0. 927498 0.904437 0.881927 0.859964 0. 838545 0.817665 0. 797320 n. 7775n5 0.7582i3 0. 739438 0.721173 0.703412 0.669366 0. 637235 0. 606947 0. 578427 0. 551596 0. 526375 0. 502682 0.480435 0.459555 0. 439962 0. 421580 0. 404332 0.388148 0.372958 0.358696 0. 345301 0. 332713 0. 320876 0.294240 0. 271260 0. 251331 0. 233948 0. 218698 0. 205239 0. 193294 0. 182633 0. 173068 0. 164443 Debye Functions 1.000000 0.967083 0.934999 0. 903746 0.873322 0. 843721 0. 814940 0. 786973 0. 759813 0. 733451 0. 707878 0. 683086 0. 659064 0.635800 0. 613281 0. 570431 0. 530404 0.493083 0. 458343 0. 426057 0. 396095 0. 368324 0. 342614 0.318834 0.296859 0. 276565 0.257835 0.240554 0. 224615 0. 209916 0. 196361 0. 183860 0. 172329 0. 147243 0. 126669 0. 109727 0.095707 0. 084039 0. 074269 0. 066036 0.059053 0.053092 0.047971 Widerstandes reiner Metalle von der Temperatur, Ann. Physik. (5) 16, 530-540 (1933). x = 0 (. 1) 13 (.2) 18( 1) 20 (2) 52 (4) 80, 45. 1.000000 0.963000 0. 926999 0. 891995 0. 857985 0.824963 0. 792924 0.761859 0.731759 0. 702615 0.674416 0. 647148 0.620798 0.595351 0.570793 0. 524275 0. 481103 0. 441129 0. 404194 0. 370137 0.338793 0. 309995 0.283580 0. 259385 0. 237252 0. 217030 0. 198571 0. 181737 0. 166396 0. 152424 0. 139704 0. 128129 0. 117597 0.095241 0.077581 0. 063604 0.052506 0. 043655 0.036560 0.030840 0.026200 0. 022411 0.019296 1.000000 0. 960555 0. 922221 0.884994 0.848871 0.813846 0.779911 0.747057 0.715275 0. 684551 0.654874 0. 626228 0. 598598 0. 571967 0.546317 0.497882 n. 453131 0.4ii893 0.373984 0. 339218 0. 307405 0. 278355 0. 251879 0. 2277d2 0.205915 0. 186075 0. 168107 0.151855 0. 137169 0. 123913 0. 111957 0. 101180 0.091471 0.071228 0.055677 0. 043730 0.034541 0.027453 0.021968 0.017702 0.014368 0.011747 0.009674 [ (-;PI