книги из ГПНТБ / Харитонов, В. В. Некоторые нелинейные задачи теплопроводности
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Продолжение |
таблицы |
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m =4 |
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.18 |
.99677 |
.00325 |
.99678 |
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0,6 |
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.00326 |
.99678 |
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.00326 |
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.99679 |
.00327 |
.18 |
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.19 |
.99640 |
.00362 |
.99641 |
|
.00323 |
.99641 |
|
.00363 |
|
.99642 |
.00364 |
.19 |
0.20 |
0.99601 |
1.00401 |
0.99602 |
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1.00402 |
0.99603 |
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1. 00-103 |
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0.99604 ' |
1.00404 |
0.20 |
.21 |
..99560 |
.00442 |
.99561 |
|
.00443 |
.99563 |
|
.00445 |
|
.99564 |
.00446 |
.21 |
.22 |
.99517 |
.00486 |
.99519 |
|
.00487 |
.99520 |
|
.00488 |
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.99522 |
.00490 |
.22 |
.23 |
.99478 |
.00531 |
.99474 |
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.00533 |
.99476 |
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.99478 |
.00536 |
.23 |
М |
.99426 |
.00578 |
.99428 |
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.00580 |
.99430 |
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.00582 |
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.99432 |
.00584 |
.24 |
.25 |
.99377 |
.00627 |
.99380 . |
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.00630 |
.99382 |
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.00632 |
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.99385 |
.00635 |
.25 |
.26 |
.99327 |
.00679 |
.99330 |
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.00682 |
.99333 |
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.00685 |
|
.99335 |
.00688 |
.26 |
.27 |
.99274 |
.00732 |
.99278 |
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.00736 |
.99281 |
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.00739 |
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.99284 |
.00743 |
.27 |
.28 |
.99220 |
.00788 |
.99224 |
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.00792 |
.99227 |
. |
.00796 |
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.99231 |
.00800 |
.28 |
.29 |
.99163 |
.00846 |
.99168 |
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.00850 |
.99172 |
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.00854 |
|
.99176 |
.00860 |
.29 |
.30 |
.99105 |
.00905 |
.99110 |
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.99115 |
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.00915 |
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.99120 |
.00921 |
.30 |
.31 |
.99045 |
.00967 |
.99050 |
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.00973 |
.99056 |
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.99062 |
.00985 |
.31 |
.32 |
.98982 |
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.98989 |
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.98995 |
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.01044 |
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.01051 |
.32 |
.33 |
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.01096 |
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.98933 |
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.01112 |
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.34 |
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.01164 |
.98860 |
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.98869 |
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.01181 |
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.98877 |
.01190 |
.34 |
.35 |
.98784 |
.01234 |
.98794 |
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.98803 |
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.35 |
.36 |
.98714 |
.01307 |
.98725 |
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.01328 |
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.36 |
.37 |
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.37 |
.38 |
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.39 |
.98493 |
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.01565 |
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.01581 |
.39 |
0.40 |
0.98416 |
1.01616 |
0.98432 |
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1.01633 |
0.98447 |
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1.01649 |
|
0.98462 |
1.01666 |
0.40 |
.41 |
.98337 |
.01700 |
.98354 |
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.01717 |
.98371 |
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.01735 |
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.98371 |
.01754 |
.41 |
.42 |
.98255 |
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.98274 |
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,98298 |
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.01823 |
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.01844 |
,42 |
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.01892 |
.98214 |
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.01915 |
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.98234 |
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.43 |
.44 |
.98087 |
.01960 |
.98110 |
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.98132 |
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.98155 |
.02033 |
.44 |
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.98000 |
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.98025 |
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.98050 |
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.45 |
.46 |
.97912 |
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.02232 |
.46 |
.47 |
.97821 |
.02240 |
.97851 |
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.02271 |
.97880 |
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.02303 |
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.97908 |
.02336 |
.47 |
.48 |
.97729 |
.02337 |
.97761 |
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.02372 |
.97793 |
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.48 |
.49 |
.97635 |
.02437 |
.97670 |
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.97704 |
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.02512 |
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.97737 |
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.49 |
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.97539 |
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.97577 |
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.97613 |
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.50 |
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.97441 |
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.97482 |
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.51 |
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.97341 |
. .02750 |
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.52 |
.53 |
.97240 |
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.97288 |
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.97238 |
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.54 |
.55 |
.97032 |
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.57 |
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0.60 |
0.96480 |
1.03682 |
0.96558 |
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1.03767 |
0.96632 |
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1.03855 |
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1.03946 |
0.60 |
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Продолжение таблицы |
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ш= [ |
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m =3 |
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m = 4 |
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І^о 1—0,6 |
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.78 |
.94143 |
.06320 |
.94358 |
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.06570 |
.94560 |
.06837 |
.94751 |
.07122 |
.78 |
.79 |
.93998 |
.06489 |
.94223 |
|
.06753 |
.94435 |
■ .07035 |
.94636 |
.07337 |
.79 |
0.80 |
0.93851 |
1.06661 |
0.94088 |
|
1.06939 |
0.94310 |
1.07237 |
0.94520 |
1.07556 |
0.80 |
.81 |
.93703 |
.06835 |
.93951 |
|
.07128 |
.94184 |
.07442 |
.94403 |
.07780 |
.81 |
.82 |
.93553 |
.07012 |
.93813 |
• |
.07320 |
.94057 |
'.07651 |
.94286 |
.08008 |
.82 |
.83 |
.93402 |
.07191 |
.93674 |
.07516 |
.93929 |
.07865 |
.94168 |
.08242 |
.83 |
|
.84 |
.93249 |
.07374 |
.93534 |
|
.07714 |
.93801 |
.08082 |
.94050 |
.08460 |
.84 |
.85 |
.93095 |
.07558 |
.93393 |
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.07916 |
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.93932 |
.08724 |
.85 |
.86 |
.92939 |
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.93250 |
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.08528 |
.93813 |
.08971 |
.86 |
.87 |
.92781 |
.07935 |
.93107 |
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.08330 |
.93410 |
.08758 |
.93693 |
.09225 |
.87 |
.88 |
.92623 |
.08127 |
.92963 |
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.08542 |
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.08992 |
.93574 |
.09484 |
.88 |
.89 |
.92462 |
.08322 |
.92817 |
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.08757 |
.93147 |
.09230 |
.93454 |
.09748 |
.89 |
.90 |
.92301 |
.08520 |
.92671 |
|
.08975 |
.93015 |
.09472 |
.93334 |
.10018 |
.90 |
.91 |
.92138 |
.08720 |
.92524 |
|
.09197 |
.92882 |
.09719 |
.93214 |
.10293 |
.91 |
.92 |
.91974 |
.08923 |
.92376 |
|
.09922 |
.92748 |
.09970 |
.93093 |
.10574 |
.92 |
.93 |
.91808 |
.09128 |
.92227 |
|
.09651 |
.92614 |
.09614 |
.92973 |
.10861 |
.93 |
.94 |
.91640 |
.09336 |
.92077 |
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.10487 |
.92852 |
.11154 |
.84 |
.95 |
.91471 |
.09547 |
.91926 |
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.10752 |
.92730 |
.11453 |
.95 |
.96 |
.91301 |
.09761 |
.91775 |
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.10359 |
.92209 |
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.92609 |
.11758 |
.96 |
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0.99701 |
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,32 |
.99237 |
.00773 |
.99242 |
,00778 |
.99247. |
.00783 |
.99251 |
.00788 |
,32 |
H>n
1
sc s i я с е oi j
|
|
m= |
1 |
|
m=2 |
in —3 |
|
|
|
m—4 |
Продолжение таблицы |
|||
|
|
|
|
|
|
|
|
|
||||||
|
u + |
|
и . |
“ + |
|
и . |
“ + |
и. |
|
“ + |
|
и. |
|
|
.33 |
|
|
.00822 |
|
|
Ы =0,7 |
|
|
|
|
|
|
|
|
.99189 |
|
.99194 |
|
.00828 |
.99200 |
.00834 |
|
.99205 |
|
.00839 |
|
.33 |
||
.34 |
.99139 |
|
.00873 |
.99145 |
|
.00880 |
.99152 |
.00886 |
|
.99158 |
■ |
.00893 |
|
.34 |
.35 |
.99088 |
|
.00926 |
.99095 |
|
.00940 |
.99102 |
.00948 |
|
.99109 |
.00948 |
|
.35 |
|
.36 |
.99036 |
|
.00980 |
.99044 |
|
.00988 |
. .99051 |
.00996 |
|
.99059 |
|
.01004 |
|
.36 |
.37 |
.98982 |
|
.01036 |
.98991 |
|
.01045 |
.98999 |
.01054 |
|
.99008 |
|
.01063 |
|
■ .37 |
.38 |
.98927 |
|
.01093 |
.98936 |
|
.01103 |
.98946 |
.01113 |
|
.98955 |
|
.01123 |
|
.38 |
.39 |
.98870 |
|
.01152 |
.98881 |
|
.01163 |
.98891 |
.01174 |
|
.98902 |
|
.01185 |
|
.39 |
0.40 |
0.98812 |
|
1 . 0 1 2 1 2 |
.098824 |
|
1.01224 |
0.98835 |
1.01237 |
|
0.98847 |
' |
1.01249 |
|
0.40 |
.41 |
.98752 |
|
.01274 |
.98765 |
|
.01288 |
.98778 |
.01301 |
|
.98791 |
|
.01315 |
|
.41 |
.42 |
.98691 |
|
.01338 |
.98706 |
|
.01353 |
.98720 |
.01368 |
|
.98734 |
|
.01383 |
|
.42 |
.43 |
.98629 |
|
.01403 |
.98645 |
|
.01419 |
.98660 |
.01436 |
|
.98675 |
|
.01453 |
|
.43 |
.44 |
.98565 |
|
.01470 |
.98583 |
|
.01488 |
.98599 |
.01506 |
' |
.08616 |
|
.01525 |
|
.44 |
.45 |
.98500 |
|
.01538 |
.98519 |
|
.01558 |
.98538 |
.01578 |
.98556 |
|
.01598 |
|
.45 |
|
.46 |
.98434 |
|
.01608 |
.98454 |
|
.01630 |
.98474 |
.01652 |
■ |
.98494 |
|
.01674 |
|
.46 |
.47 |
.98366 |
|
.01680 |
.98388 |
|
.01703 |
.98410 |
.01727 |
.98432 |
|
.01752 |
|
.47 |
|
.48 |
.98297 |
|
.01753 |
.98321 |
|
.01779 |
.98345 |
.01805. |
|
.98368 |
|
.01831 |
|
.48 |
.49 |
.98226 |
|
.01828 |
.98252 |
|
,01856 |
.98278 |
.01884 |
|
.98303 |
|
.01913 |
|
.49 |
.50 |
.98154 |
|
.01905 |
' .98182 |
|
.01935 |
.98240 |
.01966 |
|
.98238 |
|
.01997 |
|
.50 |
.51 |
.98081 |
|
.01983 |
.9811.1 |
|
.02015 |
.98142 |
.03049 |
|
.97171 |
|
.02083 |
|
.51 |
.52 |
.98006 |
|
.02063 |
.98039 |
|
.02098 |
.98072 |
.02134 |
|
.98103 |
|
.02171 |
|
.52 |
.53 |
.97930 |
|
.02144 |
.97966 |
|
.02182 |
.98001 |
.0 2 2 2 2 |
|
.98035 |
|
.02262 |
|
.53 |
.54 |
.97852 |
|
.02227 |
.97891 |
|
.02268 |
.97929 |
.02312 |
|
.97965 |
|
.02354 |
|
.54 |
.55 |
.97774 |
|
.02312 |
.97815 |
|
.02357 |
.97855 |
.02402 |
|
.97895 |
|
.02449 |
|
.55 |
.56 |
.97694 |
|
.02400 |
.97738 |
|
.02446 |
.97781 |
.02496 |
|
.97823 |
|
.02546 |
|
.56 |
.57 |
.97612 |
|
.02487 |
.97660 |
|
.02538 |
.97706 |
.02591 |
|
.97751 |
|
.02646 |
|
.57 |
.58 |
.97529 |
|
.02577 |
.97581 |
|
.02632 |
.97630 |
.02687 |
|
.97678 |
|
.02747 |
|
.58 |
.59 |
.97445 |
|
.02668 |
.97500 |
|
.02727 |
.97553 |
.02788 |
|
.97604 |
|
.02851 |
|
.59 |
ж* . ■ |
------ f - |
- |
|
|
' |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
0.60 |
0.97360 |
|
1.02761 |
0.97418 |
|
1.28825 |
0.97475 |
1.02890 |
|
0.97530 |
|
1.02958 |
|
0.60 |
.61 |
.97273 |
|
.02856 |
.97336 |
|
.02924 |
.97396 |
.02994 |
|
.97454 |
|
.03067 |
|
.61 |
.62 |
.97185 |
|
.02953 |
.97252 |
|
.03026 |
.97316 |
.03101 |
|
.97378 |
|
.03178 |
|
.62 |
.63 |
.97096 |
|
.03051 |
.97167 |
|
.03129 |
.97235 |
.03209 |
|
.97301 |
|
.03292 |
|
.63 |
.64 |
.97006 |
|
.03152 |
.97081 |
|
.03234 |
.97153 |
.03320 |
|
.97223 |
|
.03409 |
|
.64 |
.65 |
.96914 |
|
.03253 |
.96994 |
|
.03341 |
.97070 |
.03433 |
|
.97145 |
|
.03528 |
|
.65 |
.66 |
.96821 |
|
.03357 |
.96905 |
|
.03451 |
.96987 |
.03548 |
|
.97065 |
|
.03650 |
|
.66 |
67 |
.96726 |
|
.03462 |
.96816 |
’ |
.03562 |
.96902 |
.03666 |
|
.96986 |
|
.02774 |
|
.67 |
.68 |
.96631 |
|
.03570 |
.96726 |
.03675 |
.96817 |
.03786 |
|
.96905 |
|
.03901 |
|
.68 |
|
.69 |
.96534 |
_ |
.03678 |
.96635 |
|
.03791 |
.96731 |
.03908 |
|
.96824 |
|
.04031 |
|
.69 |
.70 |
.96436 |
.03789 |
.96542 |
|
.03908 |
.96644 |
.04033 |
|
.96742 |
|
.04164 |
|
.70 |
|
.71 |
.96337 |
|
.03902 |
.96449 |
|
.04028 |
.96557 |
.04160 |
|
.96660 |
|
.04299 |
|
.71 |
.72 |
.96236 |
|
.04016 |
.96355 |
|
.04150 |
.96468 |
.04290 |
|
.96577 |
|
.04438 |
|
.72 |
.73 |
.96134 |
|
.04132 |
.96260 |
|
.04274 |
.96379 ' |
' .04423 |
|
.96494 |
|
.04579 |
|
.73 |
.74 |
.96031 |
|
.04250 |
.96163 |
|
.04400 |
.96289 |
.04557 |
|
.96410 |
|
.04724 |
|
.74 |
.75 |
.95927 |
|
.04369 |
.96066 |
|
.04528 |
.96199 |
.04695 |
|
.96325 |
|
.04871 |
• |
.75 |
.76 |
.95822 |
|
.04491 |
.95968 |
|
.04658 |
.96107 |
.05022 |
|
.96240 |
|
.05022 |
.76 |
|
.77 |
.95715 |
|
.04614 |
.95869 |
|
.04791 |
.96015 |
.04978 |
|
.96155 |
|
.05175 |
|
.77 |
.78 |
.95608 |
|
.04740 |
.95769 |
|
.04926 |
.95923 |
.05123 |
|
.96069 |
|
.05332 |
|
.78 |
.79 |
.95499 |
|
.04867 |
.95669 |
|
.05063 |
.95830 |
.05271 |
|
.95983 |
|
.05493 |
|
.79 |
0.80 |
0.95389 |
1.04996 |
0.95567 |
|
1.05202 |
0.95736 |
1.05467 |
|
0.95896 |
|
1.05656 |
|
0.80 |
|
.81 |
.95277 |
|
.05126 |
.95464 |
|
.05344 |
.95641 |
.05576 |
|
.95809 |
|
.05823 ' |
|
.81 |
.82 |
.95165 |
|
.05259 |
.95361 |
|
.05488 |
.95546 |
.05733 |
|
.95722 |
|
.05994 |
|
.82 |
.83 |
.95051 |
|
.05494 |
.95257 |
|
.05635 |
.95451 |
.05892 |
|
.95634 |
|
.06168 |
|
.83 |
.84 |
.94937 |
|
.05530 |
.95152 |
|
.05784 ' |
.95355 |
.06055 |
|
.95546 |
|
.06345 |
|
.84 |
.85 |
.94821 |
|
.05668 |
.950461 |
|
.05935 |
.95258 |
.06220 |
|
.95458 |
|
.06526 |
|
.85 |
.86 |
.94704 |
|
.05809 |
.94940 |
|
.06089 |
.95161 |
.06389 |
|
.95369 |
|
.06711 |
|
.86 |
.87 |
.94586 |
|
.05951 |
.94832 |
|
.06245 |
.95063 |
.06560 |
|
.95280 |
|
.06900 |
|
.87 |
.88 |
.94467 |
|
.06095 |
.94724 |
|
.06403 |
.94965 |
.06735 |
|
.95191 |
|
.07093 |
|
.88 |
.89 |
.94347 |
|
.06241 |
.94615- |
|
.06564 |
.94867 |
.06913 |
|
.95102 |
■ |
.07289 |
|
.89 |
.90 |
.94226 |
|
.06390 |
.94506 |
|
.06728 |
.94768 |
.07094 |
|
.95013 |
.07490 |
|
.90 |
|
.91 |
.94103 |
|
.06540 |
.94396 |
|
.06894 |
.94668 |
.07278 |
|
.94923 |
|
.07694 |
|
.91 |
.92 |
.93980 |
|
.06692 |
.94285 |
|
.07063 |
.94568 |
.07465 |
|
.94834 |
|
.07903 |
|
.92 |
.93 |
.93856 |
|
.06846 |
.94173 |
|
.07234 |
.94468 |
.07656 |
|
.94744 |
|
.08116 |
’ |
.93 |
.94 |
.93730 |
|
.07002 |
.94061 |
|
.07409 |
.94368 |
.07850 |
|
.94654 |
|
.08334 |
.94 |
л.
о>
|
|
|
|
|
|
|
|
Продолжение |
таблицы |
|
|
п г ~ 1 |
|
т — 2 |
/ л = 3 |
|
|
т= 4 |
|
|
“ + |
и. |
и + |
|
“ + |
|
|
и. |
|
|
|
|
|
|
|
|
|||
|
|
|
|
І*О І= 0 ,7 |
|
|
|
|
|
.95 |
.93604 |
.07160 |
.93948 |
.07585 |
.94267 |
.08048 |
.94564 |
.08555 |
.95 |
.96 |
.93476 |
.07321 |
.93834 |
.07765 |
.94166 |
.08249 |
.94474 |
.08782 |
.96 |
.97 |
.93347 |
.07483 |
.93720 |
.07947 |
.94064 |
.08454 |
.94384 |
.09013 |
.97 |
.98 |
.93218 |
.07647 |
.93605 |
.08132 |
.93963 |
.08663 |
.94294 |
.09249 |
.98 |
.99 |
.93087 |
.07814 |
.93490 |
.08319 |
.93861 |
.08875 |
.94204 |
.09489 |
.99 |
1.00 |
.92956 |
.07982 |
.93374 |
.08510 |
.93758 . |
.09091 |
.94114 |
.09735 |
1.00 |
|
|
|
|
N - |
0,8 |
|
|
|
|
0.00 |
1.00000 |
1.00000 |
1.00000 |
1.00000 |
.01 |
0.99999 |
.00001 |
0.999991 |
.00001 |
.02 |
.99998 |
.00002 |
.99998 |
.00002 |
.03 |
.99996 |
.00005 |
.99996 |
.00005 |
.04 |
.99992 |
.00008 |
.99992 |
.00008 |
.05 |
.99988 |
.00013 |
.99988 |
.00013 |
.06 |
.99982 |
.00018 |
.99982 |
.00018 |
.07 |
.99976 |
.00025 |
.99976 |
.00025 |
.08 |
.99968 |
.00032 |
99968 |
.00032 |
.09 |
.99960 |
.00041 |
.99960 |
.00041 |
.10 |
.99950 |
.00050 |
.99950 |
.00050 |
.11 |
.99940 |
.00061 |
.99940 |
.00061 |
.12 |
.99928 |
.00072 |
.99928 |
.00072 |
.13 |
.99916 |
.00085 |
.99916 |
.00085 |
.14 |
.99902 |
.00098 |
.99902 |
.00098 |
.15 |
.99888 |
.00113 |
.99888 |
.00113 |
.16 |
.99872 ■ |
.00128 |
.99872 |
.00128 |
.17 |
.99856 |
.00145 |
.99856 |
.00145 |
|
V ...................... |
----- |
|
................ . . . ,— щ А — |
|
|
|
|
|
|
|
.18 |
.99838 |
|
.00162 |
.99838 |
.00162 |
.19 |
.99820 |
|
.00181 |
.99820 |
.00181 |
0.20 |
0.99800 |
|
1.00201 |
0.99801 |
1.00201 |
.21 |
.99780 |
|
.00221 |
.99781 |
.00222 |
Т > |
.99759 |
|
.00243 |
.99760 |
.00244 |
.23 |
.99736 |
|
.00265 |
.99737 |
.00266 |
.24 |
.99713 |
|
.00289 |
.99714 |
.00290 |
.25 |
.99689 |
. |
.00314 |
.99690 |
.00315 |
.26 |
.99663 |
|
.00339 |
.99665 |
.00341 |
.27 |
.99637 |
|
.00366 |
.99639 |
.00368 |
.28 |
.99610 |
|
.00394 |
.99612 |
.00396 |
.29 |
.99582 |
|
.00423 |
.99584 |
.00425 |
.30 |
.99553 |
|
.00453 |
.99555 |
.00455 |
.31 |
.99522 |
|
.00483 |
.99525 |
.00486 |
.32 |
.99491 |
|
.00515 |
.99495 |
.00519 |
.33 |
.99459 |
|
.00548 |
.99463 |
.00552 |
.34 |
.99426 |
|
.00582 |
.99430 |
.00586 |
.35 |
.99392 |
|
.00617 |
.99397 |
.00622 |
.36 |
.99357 |
|
.00653 |
.99352 |
.00659 |
.37 |
.99321 |
|
.00690 |
.99327 |
.00696 |
.38 |
.99284 |
|
.00729 |
.99291 |
.00735 |
.39 |
.99247 |
|
.00768 |
.99254 |
.00775 |
0.40 |
0.99208 |
|
1.00808 |
0.99216 . |
1.00816 |
.41 |
.99168 |
|
.00849 |
.99177 |
.00858 |
.42 |
.99128 |
|
.00892 |
.99137 |
.00902 |
.43 |
.99086 |
|
.00935 |
.99097 |
.00946 |
.44 |
.99044 |
|
.00980 |
.99055 |
.00991 |
.45 |
.99000 |
|
.01025 |
.99013 |
.01039 |
.46 |
.98956 |
. |
.01072 |
.98970 |
.01086 |
.47 |
.98911 |
|
.01120 |
.98926 |
.01136 |
.48 |
.98864 |
|
.01169 |
.98881 |
.01186 |
.49 |
.98817 |
|
.01219 |
.98835 |
.01237 |
.50 . |
.98769 |
|
.01270 |
.98788 |
.01290 |
.51 |
.98720 |
|
.01322 |
.98741 |
.01344 |
1.00000 |
1.00000 |
1.00000 |
1.00000 |
0.00 |
0.99999 |
.00001 |
0.99999 |
.00001 |
.01 |
.99998 |
.00002 |
.99998 |
.00002 |
.02 |
.99996 |
.00005 |
.99996 |
.00005 |
.03 |
.99992 |
.00008 |
.99992 |
.00008 |
.04 |
.99988 |
.00013 |
.99988 |
.00013 |
.05 |
.99982 |
.00018 |
.99982 |
.00018 |
.06 |
.99976 |
.00025 |
.99976 |
.00025 |
.07 |
.99968 |
:00032 |
.99968 |
.00032 |
.08 |
.99960 |
.00041 |
.99966 |
.00041 |
.09 |
.99950 |
.00050 |
.99950 |
.00050 |
.10 |
.99940 |
.00061 |
.99940 |
.00061 |
.11 |
.99928 |
.00072 |
.99928 |
.00072 |
.12 |
.99916 |
.00085 |
.99916 |
.00085 |
.13 |
.99902 |
.00098 |
.99902 |
.00098 |
.14 |
.99888 |
.00113 |
.99888 |
.00113 |
.15 |
.99873 |
.00129 |
.99873 |
.00129 |
.16 |
.99856 |
.00145 |
.99856 |
.00145 |
.17 |
-TU |
|
|
|
- - “I |
.99839 |
.00163 |
.99839 |
.00163 |
.18 |
.99821 |
.00182 |
.99821 |
.00182 |
.19 |
.99801 |
1.00202 |
0.99802 ' |
1.00202 |
0.20 |
.99781 |
.00223 |
.99782 |
.00223 |
.21 |
.99760 |
.00244 |
.99761 |
.00245 |
.22 |
.99738 |
.00267 |
.99739 |
.00268 |
.23 |
.99715 |
.00291 |
.99716 |
.00292 |
.24 |
.99691 |
.00316 |
.99692 |
.00317 |
.25 |
.99666 |
.00342 |
.99668 |
.00344 |
.26 |
.99640 |
.00370 |
.99642 |
.00371 |
.27 |
.99614 |
.00398 |
.99616 |
.00399 |
.28 |
.99586 |
.00427 |
.99588 |
.00429 |
.29 |
.99558 |
.00458 |
.99560 |
.00460 |
.30 |
.99528 |
.00489 |
.99531 |
.00492 |
.31 |
.99498 |
.00522 |
.99501 |
.00525 |
.32 |
.99466 |
.00556 |
.99476 |
.00559 |
.33 |
.99434 |
.00591 |
.99438 |
.00595 |
.34 |
.99401 |
.00627 |
.99406 |
.00632 |
.35 |
.99368 |
.00664 |
.99373 |
.00669 |
.36 |
.99333 |
.00702 |
.99338 |
.00708 |
.37 |
.99297 |
.00742 |
.99304 |
.00749 |
.38 |
.99261 |
.00783 |
.99268 |
.00290 . |
.39 |
0.99224 |
1.00824 |
0.9923Г |
1.00833 |
0.40 |
.99186 |
.00867 |
.99194 |
.00877 |
.41 |
.99147 |
.00912 |
.99156 |
.00922 |
.42 |
.99107 |
.00957 |
.99117 |
.00968 |
.43 |
.99066 |
.01004 |
.99078 |
.01016 |
.44 |
.99025 |
.01052 |
.99037 |
.01065 |
.45 |
.98983 |
.01101 |
.98996 |
.01116 |
.46 |
.98940 |
.01151 |
.98955 |
.01168 |
.47 |
.98897 |
.01203 |
.98912 |
.01221 |
.48 |
.98852 |
.01256 |
.98869 |
.01275 |
.49 |
.98807 |
.01310 |
.98825 |
.01331 |
.50 |
.98761 |
.01366 ' |
.98781 |
.01388 |
,51 |
N1=1
X
|
|
“ + |
1 |
|
.52 |
.98671 |
|
|
.53 |
.98620 |
|
|
.54 |
.98568 |
|
|
.55 |
.98516 |
|
|
.56 |
.98462 |
|
|
.57 |
.98408 |
|
' |
.58 |
. .98353 |
|
|
.59 |
.98297 |
• |
|
0.50 |
0.98240 |
|
' |
.61 |
.98182 |
|
|
.62 |
.98124 |
|
|
.63 |
.98064 |
|
|
.64 |
.98004 |
|
|
.65 |
.97943 |
|
|
.66 |
.97881 |
|
|
.67 |
.97818 |
|
|
.68 |
.97754 |
|
|
.69 . |
.97689 |
' |
|
.70 |
.97624 |
|
|
.71 |
.97558 |
|
|
.72 |
.97491 |
|
|
.73 |
.97423 |
|
|
.74 |
.97354 |
|
-
.75 |
.97285 |
.76 |
.97215 |
.77 |
.97144 |
78 |
.97072 • |
.79 |
.96999 |
0.800.96926
.96852.81
.82 |
.96777 |
.83 |
.96701 |
.84 |
.96624 |
.85 |
.96547 |
.86 |
.96469 - |
.87 |
.96391 |
.88 |
.96311 |
.89 |
.96231 |
.90 |
.96150 |
.91 |
.96069 |
.92 |
.95987 |
.93 |
.95904 |
.94 |
.95820 |
.95 |
. 95736' |
.96 |
.95651 |
.97 |
.95565 |
.98 |
.95479 |
.99 |
.95392 |
1.00 |
.95304 |
и .
.01375
.01429
.01485
.01541
.01599
.01658
.01718
.01779
1.01841
.01904
.01969
.02034
.02101
.02169
.02238
.02308
.02380
.02452
.02526
.02601
.02677
.02755
.02833
-——-<Ѵу---------
.02913
.02944
.03076
.03160
.03244
1.03330
.03418
.03506
.03596
. 03687'
.03779
.03873
.03967
.04046
.04161
.04260
.04360
.04461
.04564
.04668
.04774
.04880
.04989
.05098
.05209
.05321
|
п и =2 |
|
пи=3 |
и+ |
и . |
“ + |
и . |
|
|
||
|
\ь 0 = |
0,8 |
|
.98643 |
.01399 |
.98715 |
.01423 ' |
.98644 |
.01455 |
.98667 |
.01481 |
.98594 |
.01512 |
.98619 |
.01540 |
.98543 |
.01571 |
.98571 |
.01601 |
.98492 |
.01631 |
.98521 |
.01663 |
.98440 |
.01692 |
.98471 |
.01727 |
.98387 |
.01754 |
.98420 |
.01792 |
.98333 |
.01818 |
.98369 |
.01858 |
0.98279 |
1.01883 |
0.98317 |
1.01926 |
.98224 |
.01949 |
.98264 |
.02000 |
.98168 |
.02017 |
.98211 |
.02066 |
.98111 |
.02086 |
.98157 |
.02139 |
.98054 |
.02156 |
.98103 |
.02212 |
.97996 |
.02227 |
.98048 |
.02288 |
.97937 |
.02300 |
.97992 |
.02364 |
.97878 |
.02379 |
.97936 |
.02443 |
.97818 |
.02450 |
.97879 |
.02523 |
.97757 |
.02527 |
.97822 |
.02604 |
.97695 |
.02605 |
.97764 |
.02687 |
.97633 |
.02685 |
.97706 |
.02772 |
.97570 |
.02766 |
.97647 |
.02859 |
.97507 |
..02849 |
.97587 |
.02947 |
.97443 |
.02933 |
.97528 |
.03036 |
-щі - |
t' |
----------------------------------------- |
.97378 |
|
.03018 |
|
.97467 |
.03128 |
.97313 |
|
.03105 |
|
.97407 |
.03221 |
.97247 |
|
.03193 |
|
.97345 |
.03316 |
.97180 |
|
.03283 |
|
.97284 |
.03413 |
.97113 |
|
.03375 |
|
.97222 |
.03511 |
0.97045 |
|
1.03467 |
0.97159 |
1.03612 |
|
.96977 |
■ |
.03562 |
|
.97097 |
.03714 |
.96908 |
|
.03658 |
|
.97034 |
.03818 |
.96839 |
|
.03755 |
|
.96970 |
.03924 |
.96769 |
|
.03854 |
|
.96906 |
.04032 |
.96699 |
|
.03955 |
|
.96842 |
.04142 |
.96628 |
|
.04058 |
|
.96770 |
.04254 |
.96556 |
|
.04161 |
|
.96712 |
.04368 |
.96484 |
|
.04267 |
|
.96647 |
.04484 |
.96412 |
|
.04374 |
|
.96582 |
.04602 |
.96339 |
|
.04483 |
|
.96516 |
.04722 |
.96265 |
|
.04594 |
|
.96450 |
.04844 |
.96192 |
|
.04706 |
|
.96384 |
.04969 |
.96117 |
|
. .04820 |
|
.96317 |
.05096 |
.96042 |
|
.04936 |
|
.96251 |
.05224 |
.95967 |
, |
.05054 |
|
.96184 |
.05356 |
.95892 |
|
.05173 |
' |
.96117 |
.05489 |
.95816 |
|
.05294 |
■ |
.96050 |
.05625 |
.95739 |
|
.05417 |
|
.95982 |
.05763 |
.95663 |
|
.05542 |
|
.95915 |
.05904 |
.95585 |
|
.05669 |
|
.95847 |
.06047 |
|
ІП ==4 |
Продолжение |
таблицы |
|
|
|
|
|
|
и . |
X |
|
“ + |
|
|
|
|
|
|
|
.98736 ■ |
.01447 |
.52 |
' |
.98690 |
.01507 |
.53 |
|
.98644 |
.01569 |
. 54, |
|
.98597 |
.01632 |
.55 |
|
.98550 |
.01697 |
.56 |
|
.98501 |
.01763 |
.57 |
|
.98453 |
.01831 |
.58 |
|
.98404 |
.01900 |
.59 |
0.98354 |
1.01970 |
0.60 |
|
|
.98304 |
.02043 |
.61 |
|
.98253 |
.02118 |
.62 |
|
.98202 |
.02193 |
.63 |
|
.98150 |
.02271 |
.64 |
|
.98098 |
.02350 |
.65 |
|
.98045 |
.02431 |
.66 |
|
.97992 |
.02514 |
.67 |
|
.97938 |
.02598 |
.68 |
|
.97884 |
.02685 |
.69 |
• |
.97830 |
.02773 |
.70 |
|
.97779 |
.02863 |
.71 |
|
.97720 |
.02955 |
.72 |
|
.97665 |
.03049 |
.73 |
|
.97609 |
.03145 |
.74 |
.97553 |
.03243 |
.75 |
,97497 |
.03343 |
.76 |
.97440 |
.03445 |
.77 |
.97381 |
.03549 |
.78 |
.97326 |
.03655 |
.79 |
0.97268 |
1.03764 |
0.80 |
.97211 |
.03874 |
.81 |
.97153 |
.03987 |
.82 |
.97095 |
.04103 |
.83 |
.97036 |
.04220 |
.84 |
.96978 |
.04340 |
.85 |
.96919 |
.04463 |
.86 |
.96860 |
.04588 |
.87 |
.96801 |
.04715 |
.88 |
.96742 |
.04845 |
' .89 |
.96683 |
.04983 |
.90 |
.96624 |
.05113 |
.91 |
.96565 |
.05251 |
.92 |
.96506 |
.05392 |
.93 |
.96446 |
.05535 |
.94 |
.96387 |
.05681 |
.95 |
.96327 |
.05831 |
.96 |
.96268 |
.05983 |
.97 |
.96209 |
.06138 |
.98 |
.96150 |
.06297 |
.99 |
.96090 |
.06458 |
1.00 |
со
О Г Л А В Л Е Н И Е
От редактора |
|
|
3 |
|||
Предисловие |
|
|
|
4 |
||
|
|
|
|
ГЛАВА I |
|
|
|
|
Н е к о т о р ы е з а д а ч и т е п л о п р о в о д н о с т и , |
|
|||
с в о д и м ы е к н е л и н е й н ы м д и ф ф е р е н ц и а л ь н ы м у р а в н е н и я м |
|
|||||
|
|
|
в т о р о г о п о р я д к а |
|
|
|
Введение |
|
|
|
5 |
||
§ 1. |
Теплопроводность однородного тонкого излучающе |
6 |
||||
|
|
го стержня |
|
|
||
§ 2. |
Теплопроводность двухслойного (с покрытием) тон |
16 |
||||
|
|
кого излучающего стержня |
|
|||
§ |
3. |
Расчет |
металлического дыоара |
дляжидкого гелия |
20 |
|
§ |
4. |
Теплопроводность |
тонкого излучающего диска |
25 |
||
|
|
|
|
ГЛАВА II |
|
|
|
Т е о р и я о б о б щ е н н ы х д и ф ф е р е н ц и а л ь н ы х у р а в н е н и й |
|
||||
|
|
|
Б е с с е л я н у л е в о г о п о р я д к а |
|
||
Введение |
• |
|
|
29 |
||
§ |
1. |
Интегрирование |
обобщенного |
дифференциального |
30 |
|
|
|
уравнения Бесселя без возмущающего члена |
||||
§ 2. |
Исследование решений обобщенного уравнения Бес |
34 |
||||
|
|
селя |
|
|
|
|
§ |
3. |
Решение обобщенного дифференциального уравне |
41 |
|||
|
|
ния Бесселя с полиномом в правой части |
§4. Применение теории обобщенного дифференциально го уравнения Бесселя нулевого порядка к более ши
рокому классу уравнений Эмдена—Фаулера |
43 |
ГЛАВА III |
|
И н ж е н е р н ы е п р и л о ж е н и я |
|
о б о б щ е н н ы х д и ф ф е р е н ц и а л ь н ы х у р а в н е н и й Б е с с е л я |
|
Введение |
45 |
§ 1. Характер сходимости полученных функциональных |
47 |
рядов, поведение решений |
§ 2. |
Приближенное аналитическое |
представление реше |
|
|
нии в некоторых частных случаях значении аргумен |
50 |
|
|
та и правой части уравнения |
|
|
§ 3. |
Расчет и правила пользования таблицами решении |
54 |
|
|
обобщенных уравнений Бесселя нулевого порядка |
||
Литература |
. |
56 |
|
Приложение |
. |
58 |
/
|
Х а р и т о н о в В . В ., С о р о к и н О . С. |
|
Х20 |
Некоторые нелинейные задачи теплопроводности. |
Под ред. А. Г. |
|
Шашкова. Ми., «Наука и техника», 1974. |
|
|
152 с. с ил. |
|
|
В книге рассмотрен ряд вопросов, касающихся решения нелиней |
|
|
ных дифференциальных уравнении вида ц" + —и'±и"'—0, которые |
|
|
являются определяющими при решении многих задач теплопроводно |
|
|
сти. Указанное уравнение по аналогии с уравнением |
« + “ М'±и = О |
•названо обобщенным уравнением Бесселя нулевого порядка. Приве дены решения таких уравнений в виде степенных рядов, названные обобщенными функциями Бесселя нулевого порядка, а также табли цы их значении для /п=1, 2, 3 и 4. Показана возможность примене
ния полученных результатов |
к |
решению |
более широкого |
класса |
уравнений Эмдена—Фаулера |
d { |
п du \ |
|
р—ст- |
[ х —— ± хеam = 0, случаи |
||||
|
|
dx |
|
|
Список лит.: с. 56—57 (41 назв.). Приложи |
с. 58—149. |
|
||
|
|
|
|
517 |
Валентин Викторович Харитонов] Олег Семенович Сорокин.
Некоторые нелинейные |
задачи |
теплопроводности. |
Редактор |
||||||||||
Е. |
Г. В о л к и н д . |
Обложка |
В. |
И. |
Г е р а с и м ч и к а. |
Худо |
|||||||
жественный редактор Ю. С. |
С ер гаче в . |
Технический редак |
|||||||||||
тор И. В. В о л о X а н о в и ч. |
Корректор Т. |
С. Ф и л у ш к и н а. |
|||||||||||
АТ |
03034. Сдано в набор 30.XJ-73 |
г. П одписано |
в |
печать |
4.11*74 |
г. Ф ор |
|||||||
м ат |
60Х90'/іб. Бум. тип |
№ 3. Печ. л. |
9,5. |
Уч *изд. |
л. R.5. |
И зд. |
зак . |
48. |
|||||
Тип. зак . 1208. Тираж |
1100 |
экз. |
Цена |
85 |
коп. |
И здательство |
«Н аука |
и |
|||||
техника» . Минск, Ленинский |
проспект, 68. Типография имени |
Ф ранциски |
|||||||||||
(Георгия) Скорины издательства |
«Н аука |
и техника» АН БССР и Гос |
|||||||||||
комитета СМ БССР по делам |
издательств, полиграфии и книжной тор |
||||||||||||
|
говли. Минск, |
Ленинский |
проспект, 68. |
|
|
|
|
cfuf '
85 к.