Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables (AMS55)
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MISCELLANEOUS FUNCTIONS 1003 f 3 ( 4 0. 5000 0. 4956 0. 4912 0. 4869 X 0. 1 0. 2 0. 3 0. 4 L - 2 -- 0.00 0.01 0.02 0.03 0.04 0.05 f z ( 4 0. 4431 0. 4382 0.4333 0. 4285 0.4238 0. 4191 fl(4 0. 5000 0.4914 0. 4832 0.4753 0. 4676 0.4602 f l ( 4 0. 2255 0. 2015 0. 1807 0. 1626 0. 1466 0.4826 0.5 0. 4784 11 f i ( 4 f 3 ( 4 0. 2415 0. 3025 0.2202 0. 2793 0. 2011 0. 2584 0. 1839 0. 2392 0. 1685 0. 2215 f 1 (4 0. 4263 0. 3697 0. 3238 0. 2855 0. 2531 0. 4580 0. 4204 0. 3864 0.3557 0.3278 f z ( 4 0. 3970 0.3573 0. 3227 0. 2923 0. 2654 0. 6 0. 7 0. 8 0.9 1.0 0. 50000 0.00000 0. 49019 0.08754 0.46229 0. 16933 0. 41950 0. 24139 0. 36543 0. 30136 Table 27.5 4. 0 4. 2 4. 4 4. 6 4. 8 i i 0. 30366 0. 34805 0.23746 0.38122 0. 16972 0. 40127 0. 10288 0. 40910 +O. 03892 0. 40592 -0.02062 0. 39314 -0.0746 0. 3722 -0. 1221 0.3448 -0. 1629 0. 3122 -0. 1966 0.2759 -0.2233 0. 2371 -0. 2432 0. 1971 -0. 2565 0. 1569 -0. 2639 0. 1173 -0. 2657 0.0792 5. 0 5. 2 5. 4 5. 6 5. 8 6. 0 6. 2 6. 4 6. 6 6. 8 7. 0 7. 2 7. 4 7. 6 7. 8 5 0. 0 0. 2 0. 4 0. 6 0. 8 1. 0 1. 2 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 -0.2626 -0.2552 -0.2441 -0. 2299 -0. 2132 -0. 1945 -0. 1745 -0. 1536 -0.1322 -0. 1108 -0.0896 -0.0691 -0.0493 -0.0307 -0.0132 +O. 00286 0.01749 0.03061 0.04220 0.05224 0.0430 +O. 0094 -0.0214 -0.0490 -0.0734 -0.0944 -0.1120 -0. 1263 -0. 1374 -0. 1455 -0. 1507 -0.1533 -0. 1535 -0. 1515 -0. 1476 -0. 14211 -0. 13518 -0. 12709 -0. 11805 7 0 . 10830 8. 0 8. 5 9. 0 9. 5 10. 0 10. 5 11. 0 11. 5 12. 0 12. 5 13. 0 13. 5 14. 0 14. 5 15. 0 16. 0 17. 0 18. 0 19. 0 20. 0 - 3?f3(iX) 0.06078 0.07562 0.08221 0.08191 0.07626 0.06684 0.05507 0. 04224 0.02937 0.01727 $0.00650 -0.00259 -0.00982 -0.01517 -0.01872 -0.02118 -0.01906 -0.01435 -0.00879 -0. 00360 “-3’1 Compiled from U. E. Kruse and N. F. Ramsey, The integral a exp -yl+i dy, J. Math. Phys. 30,40 (1951) (with permission). s0-y ( Y> Power Series Representation 27.6.1 .~ - 27.6.2 (For y and the digamma function #(x), see chap- ter 6.) 27.6.3 f(x) =-- e-22 Ei (x2) + h e - $ s’ et2dt Relation to the Exponential Integral 1 2 0 (For Ei (2) see chapter 5 ; e-22 et2 d t , see chapter 7, -0. 09808 -0. 07131 -0.04496 -0.02082 -0.00010 +O. 01654 0.02889 0.03707 0.04146 0.04259 0.04109 0.03758 0.03268 0.02696 0.02089 +O. 00921 -0.00022 -0.00650 -0.00985 -0.01021 [ (-y] Asymptotic Representation 27.6.4 [27.14] A. ErdBlyi, Note on the paper “On a definite inte- gral” by R. H. Ritchie, Math. Tables Aids Comp. 4, 31, 179 (1950). e-”2 [27.15] E. T. Goodwin and J. Staton, Table of 1 u+z du, Quart. J. Mech. Appl. Math. 1, 319 (1948). x=0(.02)2(.05)3(.1) 10. Auxiliary function for 2=0(.01) 1. Aids Comp. 4, 30,75 (1950). [27.16] R. H. Ritchie, On a definite integral, Math. Tables