Космонавтика  Форма неполных интегралов 

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 [ 55 ] 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112

Таблица 40. Производные полиномов Лежандра P (cosd)

9 dP, (cos r>)/d9{dPj(cos/J)/di>dP3 (COS )ldd

dP (cos &)ld j dPj (cos dP (cos oi/d0 [ dP (cos &)fd9

Cf 1

Tf A

11 12 13 14

15 16 17 18° 19°

20° , 21-

; 22

! 23° 24°

, 05

: 06 7

28° 79°

30°

31° 32° 33° i 34°

1з5° 36°

i 37° 38° 39°

40° 41° 42° 43° 44

oooo

0175 0349 0523 0698

0872. 1045 1219 1392 1564

1736. 1908 2079 2250 2419

2588. 2756 2924 3090 3256

3420. 3584 3746 3907 4067

4226. 4384 4540 4695 4848

SOOO. 5150 5299 5U6 5592

5736. 5878 6018 6157 6293

6428, 6561 6691 6820 6947

7071. -0.

- 17S 174 174 175 174

-17J 174 173 172 172

-172 171 171 149 169

-168 168 166 166 164

-164 162 161 160 1S9

-158 156 155 153. 152

-150 149 147 146 144

-142 140 139 136 135

-133 130 129 127 124

0.0000 0

0.0000

0,0000

b.oooo

0.0000

0523

-0.1047+ 3

-0,1744 +

-0,2615 +

-a,J6S9 +

-0.4877 +

1046

0,2091 5

0.3480

0,5213

0.7284

0.9692

1568

0.3129 8

0,5201

0.7775

1.0841

1,4384

2088

0.4160 11

0,6899

1.0286

1.4295

1.8896

2605

-0.5180+ 13

- 0.8567 +

-1,2728 + 85

-1.7614+ 166

i- 2.3170 + 292

3119

0,6186 16

1,0197

1.5085

2.0768

, 2,7152

3629

0.7176 1

1,1782

1.7341

2.3727

3.0795

4135

0.8148 21

1.3315

1.9481

2.4464

3.4053

4635

0,9099 и

1.4789

, i.1492

2.8954

3.6887

5130

-1.0026 + 26

-1.6199 +

- 2.3360 -1- 155

- 3.1174 + 290

- 3.9263 + 485

5619

1.0928 28

1.7537

2.5074

3.3104

4.1156

6101

1.1801 30

1.8798

2.6621

3.4729

4Д544

519.

6576

1.2643 32

1.9978

2,7993

3.6034

4.3413

042

1.3453 35

2,i069

j 2.9181

3,7008

4,3758

7500

-1.4229+ 37

-2.2069 +

- 3,0178-H 197

- 3,7646 + 341

-4.3580 + 5f7

7949 .

1.4968 39

2.2973

3.0978

3.7943

4,2885

8388

1,5668 40

2.3777

3.1576

3.7899

4.1688

8817

1,6328 42

г.447в

3.1970

3.7518

4.0012

9235

1.6946 *3

2,5073

3.2158

3,6806

3.78S4

9642

- 1.7521 + iS

- 2,5560 +

-3.2141+204

- 3.5774 + 308

-3.5338 + 388

*0037

1,8050 46

2,5937

3.1920

3.4435

3.2413

0420

1,8534 47

2,6203

3.1497

3.2804

2,9153

0790

1,8970 48

2.6358

3.0878

3.0902

2.5607

1147

1,9358 49

2,6400

3.0067

2.8749

2,1827

1491

-1,9696 + 50

-2.6330 +

- 2.9073 + 174

i- 2.6371 + 200

-1.7866+ m

1820

1.9984 51

2.6150

2.7903

2.3794

1,3782

2135

2.0222 51

2.5861

2,6568

2,1045

0.9633 +

2436

2.0408 52

2,5464

2.5077

; 1,8156

0,5476- SO

2721

2,0542 52

2.4961

2.3444

1,5155

- 0.1369

2990

- 2,0625 + 52

-2,4357 +

- 2.1680+ 117

- 1,2077 +

+ 0.2632 -

161

3244

2.0656 52

2.3654

: 1.9799

0.8953 +

0.5472

3482

2,0634 52

2,2855

1,7817

0.5815-

1.0102

3703

2.0562 51

2,1966

! 1.5748

- 0.2697

. 1,3472

3908

2,0437 51

2,0991

1 1,3608

+ 0,0370

1.6540

4095 +

- 2,0262 + 50

- 1,9934 +

-1.1413 +

-1- 0.3354-

+ 1,9267 -

4266

2.0037 50

1,8802

0.9179

0.6225

2.1620

4419

1.9761 49

. 1,7600

0,6924 +

0.8955

2.3573

4554

1,9438 48

1.6334

0,4664 -

1,1516

2,5103

4672

1,9066 47

1.5011

0,2415

1,3885

2.6196

4772 +

- 1,8648 + 45

-1.3637 +

-0.0194-

+ 1,6038 -

+ 2,6845 -

4854

1,8185 44

1.2219

+ 0.1983

1,7955

2,7047

4918

1,7678 42

1,0764

0,4100

1,9620

2,6807

4963

1,7129 41

0,9279

0,6142

2,1017

2,6138

4991

1,6539 39

0.7772

0,8094

2,2136

2,5057

5000+ fS

-r-1.S910+ 37

-0.6250 +

+ 0,9944 -

+ 2.2969-

+ 2,3589-


* jdP,(cort>)/ddjdPj(cos)/d*dP, (cos dP (cos \dP (cos d)/d& dP (cos Щ/dd j <SPj (cos d)/<ii

45

47° 48° 4У

50° 51° 52° 53° 54°

55° 5is° 5-7° 58° 59°

60° 61° 62° 3° 64°

65°

66° 67 68° 69°

70 t 71 72 73

, 74

75° 76° 77 78 79°

80° 81° 82° 83° 84°

85 . 86° 87° 88° 89°

9tf>

-0. 7071 7193 7314 7431 7547

7660. 7771 7880 7986 8090

8192. 8290 8387 8480 8572

8660.

8746

8829

8910

8988

9063.

9135

9205

9272

9336

9397.

9455

9511

9563

9613

9659 .

9703

9744

9781

9816

9848.

9877

9903

9925

9945

9962.

9976

9986

9994

9998

*0000

- 122 121 117 lit. 113

-111 109 106 104 102

97 93 92 88

86 83 SI 78 75

72 70 67 44 61

S4. 52 50 46

44 41

37 iS 32

29 26 22 20 17

14 10 8 4 2

5000+ 18

4991 18

4963 18

4918 IB

4854 18

4772+ 18

4672 18

4554 >S

4419 18

4266 17

4095+ 17

3908 17

3703 17

3482 16

3244 16

2990+ 16

3,5 329

U91 + 344 1147 3

0790 0 20

0037 3

9235 8817 8388

7949 4 7500

7041 W6 6576 6101 5619

5130 . 5

4635

*135

3629

3119

2605 2088 1568 1046 0523

0000 -0.

+ 517 520 522 523 S23

-1.5910+3Z

-0,6250 +

+ 0.9944 -

+ 2.2969-

+ 2.3589-

1.5244

0.4720

1.1677

2.3510

2.1761

1.4542

0.3190 -

1.3282

2.3757

1.9609

1.3808

0.1668

1.4749

2.3713

1.7172

1.3042

- 0.0160

1.6067 .

2.3382

1Л491

- 1,2248+ 27

+ 0.1327-

-Ц.7228-

+ 2.2771 -

+ 1.1614-

149

1.1427

0.2784

1.8225

2.1892

0.8588

1.0581

0.4205

1.9052

2.0759

0.5463 -

0.9714

0.5584

♦9

1.9704

1.9387

+ 0,2291 +

0.8828

0.6914

2.0178

1.7797

-0.0877

- 0.7925+ 14

+ 0.8188 -

+ 2.0473 -

+ 1.6008 -

- 0,3990+ 10*

0.7007

0.9Ю1

2.0587

1.4046

0,7001

0.6078

1.0547

2.0522

1.1934

0,9860

0.5140

1.1620

2,0280

0.9699

1.2524

0.4196

1.2617

1.9865

0,7369

1.4953

-0.3248 +

+ 1.3532-

+ 1.9283-

+ 0,4973 -

- 1.7109+ 306

0.2299 -

1.4361

1.8538

0.2540 -

1.8960

0.1351

1.5101

1.7640

+ 0.0098 +

2.0480

-0.0408

1.5748

1.6SS!6

- 0.2321

2.1646

+ 0,0528

1.6300

1.S418

0.4691

2.2443

+ 0.1454-

+ 1.6755-

Jt 1.4114-

- 0.6983+ 105

- 2.2861 + 384

0.2368

1.7111

1.2698

0.9170

2.2896

0.3268

1.7366

1.1183

1.1226

2.2550

37.

0.4149

1.7520

0.9580

1.3129

2.1833

0.5011

1.7573

0.7905

1.4355

2.0757

+ 0.5851 * 25

+ 1.7525 -

+ 0.6173 -

-1,6386 + 213

-1.9344+ 314

0.6666

1.7377

0.4397

1.7704

1.7617

0.7455

1.7131

0.2593 -

1.8794

1.5608

0.8214

1.6787

+ 0.0776 +

1.9645

1.3350

0.8941

1,6349

- 0.1037

2.0248

1,0882

+ 0,9636 -

+ 1.5819 -

- 0.2833 +

- 2.0596 + 258

- 0,8245+ 125

1.0295

1.5201

0.4595

2.0687

0.5483

1.0918

1.4498

0.6309

2.0520

- 0.2641 +

1.1501

1.3714

0.7961

2.0098

+ 0.0234-

1,2044

1.2854

0.9536

1.9428

0.3094

+ 1.2545-43

+ 1.1923-

- 1.1023+ 102

- 1.8519 +

+ 0.5892 -

1.3003

1.0926

1.1407

1.7382

0.8584

1.3415

0.9869

1.3679

1.6031

1.1125

1.3783

0.8758

.1.4827

1.4484

1.3473

1.4103

0.7598

1.5842

1.2760

1.5592

.+ 1.4375--

49

+ 0.6396 -

- 1.6Л5+ 149

- 1.0881 +

+ 1.7446 -

-295

1.4599

0.5160

1.7439

0.8868

1.9006

1.4774

0.3895

1.8009

0.6747

2.0246

1.4900

0.2608

1.8420

0.4544

2.1146

1,4975

0.1308

1.8667

0,2286

2.1692

+ 1.S00O-S0

O.UUUU

-1.8750+ 164

O.00UU

+ 2,1875-



Таблица 41. Функции Лежандра 2-го рода Q (X)

Q, С)

+ 0.

0.00

01000

02000

03001*

040b2

O.OS

05004

06007

07011

08017

09024

0.10

10034

11045

12058

13074

14093

0.15

15114

16139

17167

18198

19234

0.20

20273

21317

22366

23419

2U77

0.25

25541

26611

27686

28768

29857

0.30

30952

32DSS

34281

35409

36544

37689

38842

40006

41180

42365

43561

44769

45990

47223

48470

49731

51007

52298

53606

0.50

54931

+ 8,

4-1000 1000 10O1 1001 1002

+ 1001 1004 1006 1007 1010

+ 1011 1913 1№ 1019 1021

+ 1025 1028 1031 1036 1039

+ lOU 1049 1053 1058 1064

+ 1070 1075 1082 1089 1095

+ 1103 1110 1118 1124 1135

-f- 1145 1153 1164 1174 ills

+ 1196 1208 1221 1233 1247 + 14 IS 15

16 17

+ 18

- 1.

OOOOO +20

*99990 20

99960 20

99910 20

99840 20

99750 99640 99509 99359 99188

98997 98785 985S3 98300 98027

97733 97418 97082 96724 96346

95945 95523 95080 94614 94125

93615 93081 92525 91945 91342

90714 90063 89387 88687 87961

87209 86432 85628 84798 83940

83054 82140 81197 80224 79222

78188 77124 76027 74897 73733

72535 -0.

+ 20 20 20 20 20

+ 20 20 21 21 21

+ 21 21 21 21 22

+ 22 22 22 22 23

+ 23 23 23 24 24

+ 24 24 25 25 24

+ 26 26 27 27 28

+ 28 29 29

30 31

+ 31 32 33 34 35

+ 36

02000 03999 05996 07991

09983 11971 13954 15932 17903

19866 21822 23769 25706 27632

29547 31450 33339 35215 37075

38920 40748 42559 44351 46124

- 2000 1999 1997 1995 1992

- 1988 1983 1978 1971 1963

- 19S6 1947 1937 1916 191S

- 1903 1889 1876 1860 1845

+ 7 18 IS 19 20

47876 + 2t 49607 22

51316 53001 54662

56297 +

57907

59488

61041

62565

64057 + 65518 66945 68338

69695

71015 +

72297

73539

74740

75898

77012 + 78081

79102 80075 * 80997

23 24 25

26 27 29 30

12 33 34 36 37

38 40

*t 43 44

47 4

31 52

81866 + 54 -8.

+ 8.

66667

66627

66507

66307

66027

65668 65229 64711 64115 63440

62687 61856 60948 59964 58904

57769 S6559 55275 53918 52490

50990 49420 47781 46074 44301

42461 40558 38591 3656) 34474

32328 30124 27864 25552 23187

20773 18311 15803 13251 10658

08026

05357 02654 *00080 02844

05634 08446 11279 14129 16992

-SB SO SO SO

.7 79 79 78 78

-7S 77 77 76

-7J 74

73 72 71

-7 4 4 47 66

64 63 42 40 59

-57 55 54

-48 46 44 41

-37 34 32 29 26

-23 20 f7 14 10

19865 - 7 -0.

+ .

02666 05327 07978 10615

13233 15827 18393 20925 23419

25870 38274 30626 32921 35155

37324 39424

41449 43395 45259

47037

48723 50315 51808 53199

54484 55659 56721 57667 SB492

59195 59772 60220 60537 60720

60766 60674 60U1 60065 59545

58879 58066 57105 55994 54734

53323 51761 50050 48188 46177

44017 + 8.

5 10 14 19

24 29 33 38 43

- 47 52 56 61 65

70 74 78 83 8/

91 95 9

102 106

110 113 117 120

126 129 131 134 136

- 13 141 143 144 144

-147 148 149

150 150

150 ISO 150 169 148

53333 + 160

53253 160

53014 15

52615 158

52057 15Г

51343 + 155

50474 153

49452 IS*

48279 1*8

46958 145

45493 +14

43887 - 117

42144 133

40268 128

38264 121

36137 + IIS

33893 112

31537 29075 26513

106 100 93

23859 + 06 21119 7

18300 15411 12459

71 3

09451 + 4

06398 3

03306 2

00186 20

*02953 10

06103 + I

09254 -

12395 1

15518 2

18611 3

21664 24668 27611 30484 33274

35972 38567 41048 43404 45624

47698 49615 51365 52937 54322

55508 + 8.

50 60 71 02 92

103 116 125 136 1*6

157 167 17 T8S



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 [ 55 ] 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112