Pocketbook of mathematical functions:
Saved in:
| Previous Title: | Handbook of mathematical functions |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Thun [u.a.]
Deutsch
1984
|
| Edition: | Abridged ed. of "Handbook of mathematical functions" |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 468 S. graph. Darst. |
| ISBN: | 3871448184 |
Staff View
MARC
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| 245 | 1 | 0 | |a Pocketbook of mathematical functions |c Milton Abramowitz ... (ed.). Material selected by Michael Danos ... |
| 250 | |a Abridged ed. of "Handbook of mathematical functions" | ||
| 264 | 1 | |a Thun [u.a.] |b Deutsch |c 1984 | |
| 300 | |a 468 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Functions | |
| 650 | 4 | |a Mathematics -- Tables | |
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| 650 | 0 | 7 | |a Funktion |g Mathematik |0 (DE-588)4071510-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4155008-0 |a Formelsammlung |2 gnd-content | |
| 655 | 7 | |0 (DE-588)4184303-4 |a Tabelle |2 gnd-content | |
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| 700 | 1 | |a Danos, Michael |d 1922-1999 |e Sonstige |0 (DE-588)1065466110 |4 oth | |
| 780 | 0 | 0 | |i Früher u.d.T. |t Handbook of mathematical functions |
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Record in the Search Index
| _version_ | 1826823671755309056 |
|---|---|
| adam_text |
POCKETBOOKOF
MATHEMATICAL FUNCTIONS
ABRIDGED EDITION OF
HANDBOOK OF MATHEMATICAL FUNCTIONS
MILTON ABRAMOWITZ AND IRENE A. STEGUN (EDS.)
MATERIAL SELECTED BY
MICHAEL DANOS AND JOHANN RAFELSKI
1984
VERLAG HARRI DEUTSCH - THUN - FRANKFURT/MAIN
CONTENT
S
FOREWORDTOTH
E ORIGINA
L NB
S HANDBOO
K 5
PRE
F AC
E 6
2. PHYSICA
L CONSTANT
S AN
D CONVERSIO
N FACTOR
S 17
A.G
. MCNISH
, REVISE
D B
Y TH
E EDITOR
S
TABL
E 2.1
. COMMO
N UNIT
S AN
D CONVERSIO
N FACTOR
S 17
TABL
E 2.2. NAME
S AN
D CONVERSIO
N FACTOR
S
FO
R ELECTRI
C AN
D MAGNETI
C UNIT
S 17
TABL
E 2.3
. ADJUSTEDVALUESO
F CONSTANT
S 18
TABL
E 2.4. MISCELLANEOU
S CONVERSIO
N FACTOR
S 19
TABL
E 2.5
. FACTORSFORCONVERTINGCUSTOMARYU.S
. UNITSTOSIUNIT
S 19
TABL
E 2.6. GEODETI
C CONSTANT
S 19
TABL
E 2.7. PHYSICA
L ANDNUMERICALCONSTANT
S 20
TABL
E 2.8
. PERIODI
C TABL
E OF TH
E ELEMENT
S 21
TABL
E 2.9. ELECTROMAGNETI
C RELATION
S 22
TABL
E 2.10. RADIOACTIVIT
Y AN
D RADIATIO
N PROTECTIO
N 22
3. ELEMENTARY ANALYTICA
L METHOD
S 23
MILTO
N ABRAMOWIT
Z
3.1
. BINOMIA
L THEORE
M AN
D BINOMIA
L COEFFICIENTS
; ARITHMETI
C
AN
D GEOMETRI
E PROGRESSIONS
; ARITHMETIC
, GEOMETRIE
, HARMONI
E
AN
D GENERALIZE
D MEAN
S 23
3.2. INEQUALITIE
S 23
3.3
. RULE
S FO
R DIFFERENTIATIO
N AN
D INTEGRATIO
N 24
3.4. LIMITS
, MAXIM
A AN
D MINIM
A 26
3.5. ABSOLUT
E AN
D RELATIV
E ERROR
S 27
3.6. INFINIT
E SERIE
S 27
3.7. COMPLE
X NUMBER
S AN
D FUNCTION
S 29
3.8. ALGEBRAI
C EQUATION
S 30
3.9. SUCCESSIV
E APPROXIMATIO
N METHOD
S 31
3.10. THEOREMSONCONTINUEDFRACTION
S 32
4. ELEMENTARY TRANSCENDENTA
L FUNCTION
S 33
LOGARITHMIC
, EXPONENTIAL
, CIRCULA
R AN
D HYPERBOLI
C FUNCTION
S
RUT
H ZUCKE
R
4.1
. LOGARITHMI
C FUNCTIO
N 33
4.2. EXPONENTIA
L FUNCTIO
N 35
4.3
. CIRCULA
R FUNCTION
S 37
4.4. INVERS
E CIRCULA
R FUNCTION
S 45
4.5
. HYPERBOLI
C FUNCTION
S 49
4.6. INVERSEHYBERBOLICFUNCTION
S 52
5. EXPONENTIA
L INTEGRA
L AN
D RELATED FUNCTION
S . 56
WALTE
R GAUTSCH
I AN
D WILLIA
M F
. CAHIL
L
5.1
. EXPONENTIA
L INTEGRA
L 56
5.2. SIN
E AN
D COSIN
E INTEGRAL
S 59
TABL
E 5.1
. SINE
, COSIN
E AN
D EXPONENTIA
L INTEGRAL
S (0 X 10
) 62
TABL
E 5.2. SINE
, COSIN
E AN
D EXPONENTIA
L INTEGRAL
S FO
R LARG
E
ARGUMENT
S (10 X
) 67
TABL
E 5.3. SIN
E AN
D COSIN
E INTEGRAL
S FO
R ARGUMENT
S NX 68
TABL
E 5.4. EXPONENTIA
L INTEGRAL
S EYY(X)(0 X 2
) 69
TABL
E 5.5. EXPONENTIA
L INTEGRAL
S E
N
(X)(2 X
) 72
TABL
E 5.6. EXPONENTIA
L INTEGRA
L FO
R COMPLE
X ARGUMENT
S 73
TABL
E 5.7. EXPONENTIA
L INTEGRA
L FO
R SMAL
L COMPLE
X ARGUMENT
S
(LZL 5) 75
6. GAMMA FUNCTIO
N AN
D RELATE
D FUNCTION
S 76
PHILI
P J
. DAVI
S
6.1
. GAMM
A FUNCTIO
N 76
6.2. BET
A FUNCTIO
N 79
6.3. PSI(DIGAMMA
) FUNCTIO
N 79
6.4. POLYGAMM
A FUNCTION
S 81
6.5. INCOMPLET
E GAMM
A FUNCTIO
N 81
6.6. INCOMPLET
E BET
A FUNCTIO
N 83
7. ERROR FUNCTIO
N AN
D FRESNE
L INTEGRAL
S 84
WALTE
R GAUTSCH
I
7.1
. ERRO
R FUNCTIO
N 84
7.2. REPEATE
D INTEGRAL
S OFTH
E ERRO
R FUNCTIO
N 86
7.3. FRESNE
L INTEGRAL
S 87
7.4. DEFINIT
E AN
D INDEFINIT
E INTEGRAL
S 89
TABL
E 7.7 FRESNE
L INTEGRAL
S (0 X 5
) 92
8. LEGENDR
E FUNCTION
S 94
IREN
E A
. STEGU
N
8.1
. DIFFERENTIA
L EQUATIO
N 94
8.2. RELATION
S BETWEE
N LEGENDREFUNCTION
S 95
8.3. VALUESONTHECU
T 95
8.4. EXPLICI
T EXPRESSION
S 95
8.5. RECURRENC
E RELATION
S 95
8.6. SPECIA
L VALUE
S 96
8.7. TRIGONOMETRI
E EXPANSION
S 97
8.8. INTEGRA
L REPRESENTATION
S 97
8.9. SUMMATIO
N FORMULA
S 97
8.10. ASYMPTOTI
C EXPANSION
S 97
8.11. TOROIDA
L FUNCTION
S 98
8.12. CONICALFUNCTION
S 99
8.13. RELATIONTOELLIPTICINTEGRAL
S 99
8.14. INTEGRAL
S 99
9. BESSE
L FUNCTION
S O
F INTEGER ORDER 102
F
. W. J
. OLVE
R
BESSE
L FUNCTION
S J AN
D Y 102
9.1
. DEF INITION
S AN
D ELEMENTAR
Y PROPERTIE
S 102
9.2. ASYMPTOTI
C EXPANSION
S FO
R LARG
E ARGUMENT
S 108
9.3. ASYMPTOTI
C EXPANSION
S FO
R LARG
E ORDER
S 109
9.4. POLYNOMIA
L APPROXIMATION
S 113
9.5. ZERO
S 114
MODIFIE
D BESSE
L FUNCTION
S I AN
D K 118
9.6. DEF INITION
S AN
D PROPERTIE
S 118
9.7. ASYMPTOTI
C EXPANSION
S 121
9.8. POLYNOMIA
L APPROXIMATION
S 122
KELVI
N FUNCTION
S 123
9.9. DEFINITION
S AN
D PROPERTIE
S 123
9.10. ASYMPTOTI
C EXPANSION
S 125
9.11. POLYNOMIA
L APPROXIMATION
S 128
TABL
E 9.1
. BESSE
L FUNCTIONS
- ORDERS0,L,AND2(0 X 15
) 130
TABL
E 9.2. BESSE
L FUNCTION
S - ORDER
S 3-9(0 X 20
) 136
TABL
E 9.5. ZERO
S AN
D ASSOCIATE
D VALUE
S OF BESSE
L FUNCTION
S
AN
D THEI
R DERIVATIVE
S (0 N 8
, L S 20
) 140
TABL
E 9.8. MODIFIE
D BESSE
L FUNCTION
S OF ORDER
S 0,1
, AN
D 2 144
9
TABL
E 9.9. MODIFIEDBESSELFUNCTION
S -ORDER
S 3-9(0 X 10
) 148
TABL
E 9.12. KELVI
N FUNCTIONS-ORDER
S 0 AN
D 1(0 X 5
) 150
KELVI
N FUNCTION
S -MODULU
S AN
D PHAS
E (0 X 7
) 152
10. BESSE
L FUNCTION
S O
F FRACTIONA
L ORDER 154
H
. A
. ANTOSIEWIC
Z
10.1
. SPHERICA
L BESSE
L FUNCTION
S 154
10.2. MODIFIE
D SPHERICA
L BESSE
L FUNCTION
S 159
10.3. RICCATI-BESSE
L FUNCTION
S 161
10.4. AIR
Y FUNCTION
S 162
TABL
E 10.11. AIRYFUNCTIONS(0 X 10
) 169
TABL
E 10.12. INTEGRAL
S OF AIR
Y FUNCTION
S (0 X 10
) 172
TABL
E 10.13. ZERO
S AN
D ASSOCIATE
D VALUE
S OF AIR
Y FUNCTION
S
AN
D THEI
R DERIVATIVE
S (L S 10
) 172
11
. INTEGRAL
S O
F BESSE
L FUNCTION
S 173
YUDEL
L L
. LUK
E
11.1 SIMPL
E INTEGRAL
S OF BESSE
L FUNCTION
S 173
11.2. REPEATE
D INTEGRAL
S OF J
N
(Z
) AN
D K
0
(Z
) 175
11.3. REDUCTIO
N FORMULA
S FO
R INDEFINIT
E INTEGRAL
S 176
11.4. DEFINIT
E INTEGRAL
S 178
TABL
E 11.1
. INTEGRAL
S OF BESSE
L FUNCTION
S 182
TABL
E 11.2. INTEGRAL
S OF BESSE
L FUNCTION
S 184
12. STRUV
E FUNCTION
S AN
D RELATE
D FUNCTION
S 185
MILTO
N ABRAMOWIT
Z
12.1
. STRUV
E FUNCTIO
N HYY(Z) 185
12.2. MODIFIE
D STRUV
E FUNCTIO
N LYY(Z) 187
12.3. ANGE
R AN
D WEBE
R FUNCTION
S 187
TABL
E 12.1
. STRUV
E FUNCTION
S (0 X O
) 188
13. CONFLUEN
T HYPERGEOMETRI
C FUNCTION
S 189
LUC
Y JOA
N SLATE
R
13.1
. DEFINITION
S OF KUMME
R AN
D WHITTAKE
R FUNCTION
S 189
13.2. INTEGRA
L REPRESENTATION
S 190
13.3. CONNECTION
S WIT
H BESSE
L FUNCTION
S 191
13.4. RECURRENC
E RELATION
S AN
D DIFFERENTIA
L PROPERTIE
S 191
13.5. ASYMPTOTI
C EXPANSION
S AN
D LIMITIN
G FORM
S 193
13.6. SPECIA
L CASE
S 194
13.7. ZERO
S AN
D TURNIN
G VALUE
S 195
14. COULOM
B WAVE FUNCTION
S 198
MILTO
N ABRAMOWIT
Z
14.1
. DIFFERENTIA
L EQUATION
, SERIE
S EXPANSION
S 198
14.2. RECURRENC
E AN
D WRONSKIA
N RELATION
S 199
14.3. INTEGRA
L REPRESENTATION
S 199
14.4. BESSE
L FUNCTIO
N EXPANSION
S 199
14.5. ASYMPTOTI
C EXPANSIONS.
. ^ 200
14.6. SPECIA
L VALUE
S AN
D ASYMPTOTI
C BEHAVIO
R _ 202
14.7. US
E AN
D EXTENSIO
N OF TH
E TABLE
S 203
TABL
E 14.1
. COULOM
B WAV
E FUNCTION
S OF ORDE
R ZER
O 204
TABL
E 14.2. C
0
FA) = E-"
/2
IR(L + IR,)L 212
15. HYPERGEOMETRIC FUNCTION
S 213
FRIT
Z OBERHETTINGE
R
15.1
. GAUS
S SERIES
, SPECIA
L ELEMENTAR
Y CASES
, SPECIA
L VALUE
S OF TH
E
ARGUMEN
T 213
10
15.2. DIFFERENTIATIO
N FORMULA
S AN
D GAUSS
' RELATION
S FO
R
CONTIGUOU
S FUNCTION
S 214
15.3. INTEGRA
L REPRESENTATION
S AN
D TRANSFORMATIO
N FORMULA
S 215
15.4. SPECIA
L CASESO
F F(A
, B;C;Z),POLYNOMIAL
S AN
D LEGENDR
E FUNCTION
S 218
15.5. TH
E HYPERGEOMETRI
C DIFFERENTIA
L EQUATIO
N 219
15.6. RIEMANN'
S DIFFERENTIA
L EQUATIO
N 221
15.7. ASYMPTOTICEXPANSION
S I 222
16. JACOBIA
N ELLIPTIC FUNCTION
S AN
D THET
A
FUNCTION
S 223
L
. M. MILNE-THOMSO
N
16.1 INTRODUCTIO
N 223
16.2. CLASSIFICATIO
N OF TH
E TWELV
E JACOBIA
N ELLIPTI
C FUNCTION
S 224
16.3. RELATIO
N OF TH
E JACOBIA
N FUNCTION
S T
O TH
E COPOLA
R TRI
O 224
16.4. CALCULATIO
N OF TH
E JACOBIA
N FUNCTION
S B
Y US
E OF TH
E
ARITHMETIC-GEOMETRICMEAN(A
. G. M.) 225
16.5. SPECIA
L ARGUMENT
S 225
16.6. JACOBIA
N FUNCTION
S WHEN
M = 0OR
L 225
16.7. PRINCIPA
L TERM
S 226
16.8. CHANGEO
F ARGUMEN
T 226
16.9. RELATION
S BETWEENTH
E SQUARE
S OF TH
E FUNCTION
S 227
16.10. CHANG
E OF PARAMETE
R 227
16.11. RECIPROCA
L PARAMETE
R (JACOBI'
S REA
L TRANSFORMATION
) 227
16.12. DESCENDIN
G LANDE
N TRANSFORMATIO
N (GAUSS
' TRANSFORMATION
) 227
16.13. APPROXIMATIO
N I
N TERM
S OF CIRCULA
R FUNCTION
S 227
16.14. ASCENDIN
G LANDE
N TRANSFORMATIO
N 227
16.15. APPROXIMATIO
N I
N TERM
S OF HYPERBOLI
C FUNCTION
S 228
16.16. DERIVATIVE
S 228
16.17. ADDITIO
N THEOREM
S 228
16.18. DOUBL
E ARGUMENT
S 228
16.19. HAL
F ARGUMENT
S 228
16.20. JACOBI'
S IMAGINARYTRANSFORMATIO
N 228
16.21. COMPLEXARGUMENT
S 229
16.22. LEADIN
G TERM
S OF TH
E SERIE
S I
N ASCENDIN
G PWRS
. OF U 229
16.23. SERIE
S EXPANSIO
N I
N TERM
S OF TH
E NOME
Q 229
16.24. INTEGRAL
S OF TH
E TWELV
E JACOBIA
N ELLIPTI
C FUNCTION
S 229
16.25. NOTATIO
N FO
R TH
E INTEGRAL
S OF TH
E SQUARE
S OF TH
E
TWELV
E JACOBIA
N ELLIPTI
C FUNCTION
S 230
16.26. INTEGRAL
S I
N TERM
S OF TH
E ELLIPTI
C INTEGRA
L OF TH
E SECON
D KIN
D 230
16.27. THET
A FUNCTIONS
; EXPANSION
S I
N TERM
S OF TH
E NOME
Q 230
16.28. RELATION
S BETWEENTH
E SQUARE
S OF TH
E THET
A FUNCTION
S 230
16.29. LOGARITHMI
C DERIVATIVE
S OF TH
E THET
A FUNCTION
S 230
16.30. LOGARITHM
S OF THET
A FUNCTION
S OF SU
M AN
D DIF F ERENC
E 231
16.31. JACOBI'
S NOTATIO
N FO
R THET
A FUNCTION
S 231
16.32 CALCULATIO
N OF JACOBI'
S THET
A FUNCTIO
N 0 (U/M
) B
Y
US
E OF TH
E ARITHMETIC-GEOMETRI
C MEA
N 231
16.33. ADDITIO
N OF QUARTER-PERIOD
S T
O JACOBI'
S ET
A AN
D THET
A FUNCTION
S 231
16.34. RELATIO
N OF JACOBI'
S ZET
A FUNCTIO
N T
O TH
E THET
A FUNCTION
S 232
16.35. CALCULATIO
N OF JACOBI'
S ZET
A FUNCTIO
N Z (U/M
) B
Y US
E OF TH
E
ARITHMETIC-GEOMETRI
C MEA
N 232
16.36. NEVILLE'
S NOTATIO
N FO
R THET
A FUNCTION
S 232
16.37. EXPRESSIO
N A
S INFINIT
E PRODUCT
S 233
16.38. EXPRESSIO
N A
S INFINIT
E SERIE
S 233
11
17. ELLIPTIC INTEGRAL
S 234
L
. M. MILNE-THOMSO
N
17.1
. DEFINITIO
N OF ELLIPTI
C INTEGRAL
S 234
17.2. CANONICA
L FORM
S 234
17.3. COMPLET
E ELLIPTI
C INTEGRAL
S OF TH
E FIRS
T AN
D SECON
D KIND
S 235
17.4. INCOMPLET
E ELLIPTI
C INTEGRAL
S OF TH
E FIRS
T AN
D SECON
D KIND
S 237
17.5. LANDEN'
S TRANSFORMATIO
N 242
17.6. THEPROCESSO
F THEARITHMETIC-GEOMETRICMEA
N 243
17.7. ELLIPTI
C INTEGRAL
S OF TH
E THIR
D KIN
D 244
18. WEIERSTRAS
S ELLIPTIC AN
D RELATE
D FUNCTION
S 246
THOMA
S H
. SOUTHAR
D
18.1
. DEFINITIONS
, SYMBOLISM
, RESTRICTION
S AN
D CONVENTION
S 246
18.2. HOMOGEN
. RELATIONS
, REDUCTIO
N FORMULA
S AN
D PROCESSE
S 248
18.3. SPECIA
L VALUE
S AN
D RELATION
S 250
18.4. ADDITIO
N AN
D MULTIPLICATIO
N FORMULA
S 252
18.5. SERIE
S EXPANSION
S 252
18.6. DERIVATIVE
S AN
D DIFFERENTIA
L EQUATION
S 257
18.7. INTEGRAL
S 258
18.8. CONFORMA
L MAPPIN
G 259
18.9. RELATION
S WIT
H COMPLET
E ELLIPTI
C INTEGRAL
S K AN
D K
' AN
D THEI
R
PARAMETE
R M AN
D WIT
H JACOBI'
S ELLIPTI
C FUNCTION
S 266
18.10. RELATION
S WIT
H THET
A FUNCTION
S 267
18.11. EXPRESSIN
G ANYELLIPT
. FUNCTIO
N I
N TERM
S OF ^ AN
D 0 '. 268
18.12. CASE
A = 0 268
18.13. EQUIANHARMONICCASE(G
2
= 0,G
3
= 1) 269
18.14. LEMNISCATICCASE(G
2
= L,G
3
= 0) 275
18.15 PSEUDO-LEMNISCATICCASE(G
2
= -L,G
3
= 0) 279
19. PARABOLI
C CYLINDE
R FUNCTION
S 281
J.C.P
. MILLE
R
19.1
. TH
E PARABOLI
C CYLINDE
R FUNCTIONS
, INTRODUCTOR
Y
2
THEEQUATIO
N A
F - (-W
+ A)
Y = 0 281
DX
Z
*
19.2 T
O 19.6. POWE
R SERIES
, STANDAR
D SOLUTIONS
, WRONSKIA
N AN
D
OTHE
R RELATIONS
, INTEGRA
L REPRESENTATIONS
, RECURRENC
E RELATION
S 281
19.7. T
O 19.11
. ASYMPTOTI
C EXPANSION
S 284
19.12. T
O 19.15. CONNECTION
S WIT
H OTHE
R FUNCTION
S
2
THEEQUATIO
N -I
F + (4-X
2
- A)
Y = 0 286
DX
Z
*
19.16. T
O 19.19. POWE
R SERIES
, STANDAR
D SOLNS.
, WRONSKIA
N AN
D
OTHE
R RELATIONS
, INTEGRA
L REPRESENTATION
S 287
19.20. T
O 19.24. ASYMPTOTI
C EXPANSION
S 288
19.25. CONNECTION
S WIT
H OTHE
R FUNCTION
S 290
19.26. ZERO
S 291
19.27. BESSE
L FUNCTION
S OF ORDE
R 1/4
, 3/
4 A
S PARABOLI
C
CYLINDE
R FUNCTION
S 292
20. MATHIE
U FUNCTION
S 293
GERTRUD
E BLANC
H
20.1
. MATHIEU'
S EQUATIO
N 293
20.2. DETERMINATIO
N OFCHARACTERISTI
C VALUE
S 293
20.3
. FLOQUET'
S THEORE
M AN
D IT
S CONSEQUENCE
S 298
20.4. OTHE
R SOLUTION
S OF MATHIEU'
S EQUATIO
N 301
20.5
. PROPERTIE
S OF ORTHOGONALIT
Y AN
D NORMALIZATIO
N 303
12
20.6. SOLUTION
S OF MATHIEU'SMODIFIE
D EQUATIO
N FO
R INTEGRA
L V 303
20.7. REPRESENTATION
S B
Y INTEGRAL
S AN
D SOM
E INTEGRA
L EQUATION
S 306
20.8. OTHE
R PROPERTIE
S 309
20.9. ASYMPTOTI
C REPRESENTATION
S 311
20.10. COMPARATIV
E NOTATION
S 315
TABL
E 20.1
. CHARACTERISTI
C VALUES
, JOININ
G FACTORS
,
SOM
E CRITICA
L VALUE
S 316
TABL
E 20.2. COEFFICIENT
S A
M
ANDB
M
318
21
. SPHEROIDA
L WAFE FUNCTION
S 319
ARNOL
D N
. LOWA
N
21.1
. DEFINITIO
N OF ELLIPTICA
L COORDINATE
S 319
21.2. DEFINITIO
N OF PROLAT
E SPHEROIDA
L COORDINATE
S 319
21.3
. DEFINITIO
N OF OBLAT
E SPHEROIDA
L COORDINATE
S 319
21.4. LAPLACIA
N I
N SPHEROIDA
L COORDINATE
S 319
21.5. WAV
E EQUATIO
N I
N PROLAT
E AN
D OBLAT
E SPHEROIDA
L COORDINATE
S 319
21.6. DIFFERENTIA
L EQUATION
S FO
R RADIA
L AN
D ANGULA
R
SPHEROIDA
L WAV
E FUNCTION
S 320
21.7. PROLAT
E ANGULA
R FUNCTION
S 320
21.8. OBLAT
E ANGULA
R FUNCTION
S 323
21.9. RADIA
L SPHEROIDA
L WAV
E FUNCTION
S 323
21.10. JOININ
G FACTOR
S FO
R PROLAT
E SPHEROIDA
L WAV
E FUNCTION
S 324
21.11
. NOTATIO
N 325
TABL
E 21.1
. EIGENVALUE
S -PROLAT
E AN
D OBLAT
E 326
22. ORTHOGONA
L POLYNOMIAL
S 332
URS
. W. HOCHSTRASSE
R
22.1
. DEFINITIO
N OF ORTHOGONA
L POLYNOMIAL
S 332
22.2. ORTHOGONALIT
Y RELATION
S 333
22.3
. EXPLICI
T EXPRESSION
S 334
22.4. SPECIA
L VALUE
S 336
22.5. INTERRELATION
S 336
22.6. DIFFERENTIA
L EQUATION
S 340
22.7. RECURRENC
E RELATION
S 341
22.8
. DIFFERENTIA
L RELATION
S 342
22.9. GENERATIN
G FUNCTION
S 342
22.10. INTEGRA
L REPRESENTATION
S 343
22.11
. RODRIGUE
S FORMUL
A 344
22.12. SUMFORMULA
S 344
22.13. INTEGRAL
S INVOLVIN
G ORTHOGONA
L POLYNOMIAL
S 344
22.14. INEQUALITIE
S 345
22.15. LIMI
T RELATION
S 346
22.16. ZERO
S 346
22.17. ORTHOGONALPOLYNOMINALSO
F ADISCRETEVARIABL
E 347
22.18. US
E AN
D EXTENSIO
N OF TH
E TABLE
S 348
22.19. LEAS
T SQUAR
E APPROXIMATION
S 349
22.20. ECONOMIZATIONOFSERIE
S 350
TABL
E 22.1
. COEFFICIENT
S FO
R TH
E JACOB
I POLYNOMIAL
S P
N
(
'
P)
(X) 351
TABL
E 22.2. COEFFICIENT
S FO
R TH
E ULTRASPHERICA
L POLYNOMIAL
S
CW(X
) AN
D FO
R X
I
N TERM
S OFC G (X) 352
TABL
E 22.3
. COEFFICIENT
S FO
R TH
E CHEBYSHE
V POLYNOMIAL
S TN(X)
AN
D FO
R X
N
I
N TERM
S OFT
M
(X
) 353
TABL
E 22.5. COEFFICIENT
S FO
R TH
E CHEBYSHE
V POLYNOMIAL
S U
N
(X)
AN
D FO
R X
N
I
N TERM
S OF U
M
(X
) 353
TABL
E 22.7. COEFFICIENT
S FO
R TH
E CHEBYSHE
V POLYNOMIAL
S C
N
(X)
AN
D FO
R X
N
I
N TERM
S OF C
M
(X
) 354
13
TABL
E 22.8
. COEFFICIENT
S FO
R TH
E CHEBYSHE
V POLYNOMIAL
S S
N
(X)
AN
D FO
R X
N
I
N TERM
S OFS
M
(X
) 354
TABL
E 22.9. COEFFICIENT
S FO
R TH
E LEGENDR
E POLYNOMIAL
S P
N
(X)
AN
D FO
R X
N
I
N TERM
S OFP
M
(X
) 355
TABL
E 22.10. COEFFICIENT
S FO
R TH
E LAGUERR
E POLYNOMIAL
S L
N
(X)
AN
D FO
R X
N
I
N TERM
S OFL
M
(X
) 356
TABL
E 22.12. COEFFICIENT
S FO
R TH
E HERMIT
E POLYNOMIAL
S H
N
(X
)
AN
D FO
R X
N
I
N TERM
S OFH
M
(X
) 357
23
. BERNOULL
I AN
D EULE
R POLYNOMIAL
S -
RIEMAN
N ZETA FUNCTIO
N 358
EMILI
E V. HAYNSWORT
H AN
D KAR
L GOLDBER
G
23.1
. BERNOULL
I AN
D EULE
R POLYNOMIAL
S AN
D EULER-MACLAURI
N FORMUL
A 358
23.2. RIEMAN
N ZET
A FUNCTION
S AN
D OTHE
R SUM
S OF RECIP
. POWER
S 361
TABL
E 23.1
. COEFFS.OFTH
E BERNOULL
I AN
D EULE
R POLYNOMIAL
S 363
TABL
E 23.2. BERNOULL
I AN
D EULE
R NUMBER
S 364
24. COMBINATORIAL ANALYSI
S 365
K
. GOLDBERG
, M. NEWMA
N AN
D E
. HAYNSWORT
H
24.1
. BASI
C NUMBER
S 365
24.1.1
. BINOMIA
L COEFFICIENT
S 365
24.1.2. MULTINOMIA
L COEFFICIENT
S 366
24.1.3
. STIRLIN
G NUMBER
S OF TH
E FIRS
T KIN
D 367
24.1.4. STIRLIN
G NUMBER
S OF TH
E SECON
D KIN
D 367
24.2. PARTITION
S 368
24.2.1
. UNRESTRICTE
D PARTITION
S 368
24.2.2. PARTITION
S INTODISTINC
T PART
S 368
24.3
. NUMBE
R THEORETI
C FUNCTION
S 369
24.3.1
. TH
E MOEBIU
S FUNCTIO
N 369
24.3.2
. TH
E EULE
R TOTIEN
T FUNCTIO
N 369
24.3.3
. DIVISO
R FUNCTION
S 370
24.3.4. PRIMITIV
E ROOT
S 370
25. NUMERICA
L INTERPOLATION
, DIFFERENTIATIO
N
AN
D INTEGRATION 371
PHILI
P J
. DAVI
S AN
D IVA
N POLONSK
Y
25.1
. DIFFERENCE
S 371
25.2. INTERPOLATIO
N 372
25.3
. DIFFERENTIATIO
N 376
25.4. INTEGRATIO
N 379
25.5. ORDINAR
Y DIFFERENTIA
L EQUATION
S 390
TABL
E 25.2. N-POIN
T COEFFICIENT
S FORK-T
H ORDE
R DIFFERENTIATIO
N 392
TABL
E 25.3
. N-POIN
T LAGRANGIA
N INTEGRATIO
N COEFFICIENT
S (3
N 10) 393
TABL
E 25.4. ABSCISSA
S AN
D WEIGH
T FACTOR
S FO
R GAUSSIA
N INTEGRATIO
N 394
TABL
E 25.5
. ABSCISSA
S FO
R EQUA
L WEIGH
T CHEBYSHE
V INTEGRATIO
N 398
TABL
E 25.6. ABSCISSA
S AN
D WEIGH
T FACTOR
S FO
R LOBATT
O INTEGRATIO
N 398
TABL
E 25.7. ABSCISSA
S AN
D WEIGH
T FACTOR
S FO
R GAUSSIA
N INTEGRATIO
N
FO
R INTEGRAND
S WIT
H A LOGARITHMI
C SINGULARIT
Y 398
TABL
E 25.8
. ABSCISSA
S AN
D WEIGH
T FACTOR
S FO
R GAUSSIA
N INTEGRATIO
N
OF MOMENT
S 399
TABL
E 25.9. ABSCISSA
S AN
D WEIGH
T FACTOR
S FO
R LAGUERR
E INTEGRATIO
N 401
TABL
E 25.10. ABSCISSA
S AN
D WEIGH
T FACTOR
S FO
R HERMIT
E INTEGRATIO
N 402
TABL
E 25.11
. COEFFICIENT
S FO
R FILON'SQUADRATUR
E FORMUL
A 402
14
26. PROBABILIT
Y FUNCTION
S 403
MARVI
N ZELE
N AN
D NORMA
N C. SEVER
O
26.1
. PROBABILIT
Y FUNCTIONS
: DEF INITIQN
S AN
D PROPERTIE
S 403
26.2. NORMA
L ORGAUSSIA
N PROBABILIT
Y FUNCTIO
N 407
26.3
. BIVARIAT
E NORMA
L PROBABILIT
Y FUNCTIO
N 412
26.4. CHI-SQUAR
E PROBABILIT
Y FUNCTIO
N 416
26.5. INCOMPLET
E BET
A FUNCTIO
N 420
26.6. F-(VARIANCE-RATIO
) DISTRIBUTIO
N FUNCTIO
N 422
26.7. STUDENT'
S T-DISTRIBUTIO
N 424
26.8
. METHODSO
F GENERATIN
G RANDO
M NUMBER
S AN
D THEI
R APPLICATION
S 425
26.9. US
E AN
D EXTENSIO
N OFTHETABLE
S 429
TABL
E 26.1
. NORMA
L PROBABILIT
Y FUNCTIO
N AN
D DERIVATIVE
S (0 X 5
) 435
TABL
E 26.7. PROBABILIT
Y INTEGRA
L OF ^-DISTRIBUTIO
N (0 X
2
10) 439
27. MISCELLANEOU
S FUNCTION
S 442
IREN
E A
. STEGU
N
27.1
. DEBY
E FUNCTION
S 442
27.2. PLANCK'
S RADIATIO
N FUNCTIO
N 443
27.3
. EINSTEI
N FUNCTION
S 443
27.4. SIEVER
T INTEGRA
L 445
27.5. F
M
(X)= I T
M
E-'"-FDT AN
D RELATE
D INTEGRAL
S 445
27.6. F(*)=F" F^DT 447
27.7. DILOGARITH
M (SPENCE'
S INTEGRAL
)
J{X) =
-$LL=\
DT 448
27.8. CLAUSEN'
S INTEGRA
L AN
D RELATE
D SUMMATION
S 449
27.9. VECTOR-ADDITIO
N COEFFICIENT
S 450
SUBJEC
T INDE
X 455
INDE
X OF NOTATION
S 467
NOTATIO
N - GREE
K LETTER
S 469
MISCELLANEOU
S NOTATION
S 469 |
| any_adam_object | 1 |
| author_GND | (DE-588)110315154 (DE-588)1065466110 |
| building | Verbundindex |
| bvnumber | BV003448968 |
| callnumber-first | Q - Science |
| callnumber-label | QA47 |
| callnumber-raw | QA47.A342 1984 |
| callnumber-search | QA47.A342 1984 |
| callnumber-sort | QA 247 A342 41984 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SH 500 |
| classification_tum | MAT 330k |
| ctrlnum | (OCoLC)720926536 (DE-599)BVBBV003448968 |
| dewey-full | 511.3/319 511.3/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3/3 19 511.3/3 |
| dewey-search | 511.3/3 19 511.3/3 |
| dewey-sort | 3511.3 13 219 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | Abridged ed. of "Handbook of mathematical functions" |
| format | Book |
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| genre | (DE-588)4155008-0 Formelsammlung gnd-content (DE-588)4184303-4 Tabelle gnd-content |
| genre_facet | Formelsammlung Tabelle |
| id | DE-604.BV003448968 |
| illustrated | Illustrated |
| indexdate | 2025-03-17T07:00:16Z |
| institution | BVB |
| isbn | 3871448184 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002183428 |
| oclc_num | 720926536 |
| open_access_boolean | |
| owner | DE-384 DE-Aug4 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-20 DE-1050 DE-29T DE-29 DE-703 DE-898 DE-BY-UBR DE-706 DE-521 DE-634 DE-83 DE-188 DE-11 DE-355 DE-BY-UBR |
| owner_facet | DE-384 DE-Aug4 DE-19 DE-BY-UBM DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-20 DE-1050 DE-29T DE-29 DE-703 DE-898 DE-BY-UBR DE-706 DE-521 DE-634 DE-83 DE-188 DE-11 DE-355 DE-BY-UBR |
| physical | 468 S. graph. Darst. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Deutsch |
| record_format | marc |
| spelling | Pocketbook of mathematical functions Milton Abramowitz ... (ed.). Material selected by Michael Danos ... Abridged ed. of "Handbook of mathematical functions" Thun [u.a.] Deutsch 1984 468 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematik Functions Mathematics -- Tables Spezielle Funktion (DE-588)4182213-4 gnd rswk-swf Funktion Mathematik (DE-588)4071510-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4155008-0 Formelsammlung gnd-content (DE-588)4184303-4 Tabelle gnd-content Mathematik (DE-588)4037944-9 s DE-604 Funktion Mathematik (DE-588)4071510-3 s Spezielle Funktion (DE-588)4182213-4 s 1\p DE-604 Abramowitz, Milton 1915-1958 Sonstige (DE-588)110315154 oth Danos, Michael 1922-1999 Sonstige (DE-588)1065466110 oth Früher u.d.T. Handbook of mathematical functions DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002183428&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pocketbook of mathematical functions Mathematik Functions Mathematics -- Tables Spezielle Funktion (DE-588)4182213-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4182213-4 (DE-588)4071510-3 (DE-588)4037944-9 (DE-588)4155008-0 (DE-588)4184303-4 |
| title | Pocketbook of mathematical functions |
| title_auth | Pocketbook of mathematical functions |
| title_exact_search | Pocketbook of mathematical functions |
| title_full | Pocketbook of mathematical functions Milton Abramowitz ... (ed.). Material selected by Michael Danos ... |
| title_fullStr | Pocketbook of mathematical functions Milton Abramowitz ... (ed.). Material selected by Michael Danos ... |
| title_full_unstemmed | Pocketbook of mathematical functions Milton Abramowitz ... (ed.). Material selected by Michael Danos ... |
| title_old | Handbook of mathematical functions |
| title_short | Pocketbook of mathematical functions |
| title_sort | pocketbook of mathematical functions |
| topic | Mathematik Functions Mathematics -- Tables Spezielle Funktion (DE-588)4182213-4 gnd Funktion Mathematik (DE-588)4071510-3 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematik Functions Mathematics -- Tables Spezielle Funktion Funktion Mathematik Formelsammlung Tabelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002183428&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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