|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Nikiforov A.F., Uvarov V. — Special Functions of Mathematical Physics: A Unified Introduction with Applications |
Обсудите книгу на
Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter
|
Название: Special Functions of Mathematical Physics: A Unified Introduction with Applications
Авторы: Nikiforov A.F., Uvarov V.
Язык: 
Рубрика: Физика/
Статус предметного указателя: Готов указатель с номерами страниц
ed2k:
Год издания: 1988
Количество страниц: 427
Добавлена в каталог: 02.04.2008
Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
|
|
|
| Предметный указатель |
Absorption of light 357
Acoustic waves xv 299
Addition theorems 87 371
Airy function 226
Analytic continuation 12
Analytic continuation of Bessel functions 268
Analytic continuation of Laplace integrals 383
Analytic continuation, hypergeometric functions 262
Angular momentum addition 342
Applications of special functions 295 (Chap.V)
Approximations 355
Arsenin, V.Ya. xvii
Associated Legendre functions 79
Asymptotic formulas 97
Asymptotic formulas for Bessel functions 208
Asymptotic formulas for classical orthogonal polynomials 242
Asymptotic formulas for gamma function 376
Asymptotic formulas for Laplace integrals 380
Asymptotic properties 47
Atomic spectra xiii
Atomic units 251
Basic formulas 387—414
Bateman Project xvii
Bernoulli numbers 377
Bessel functions 201 (Chap.III) 403
Bessel functions as hypergeometric functions 288
Bessel functions with imaginary argument 223
Bessel functions, addition theorems 227 234
Bessel functions, asymptotics 208 246
Bessel functions, first kind 205
Bessel functions, functional equations 210
Bessel functions, graphs 221
Bessel functions, half-odd-integer order 220
Bessel functions, modified 223 364 407
Bessel functions, numerical calculation 355
Bessel functions, Poisson integrals 206
Bessel functions, power series 205—206 211
Bessel functions, relations for 207
Bessel functions, second kind 219
Bessel functions, Sommerfeld representations 214
Bessel functions, third kind 219
Bessel polynomials 24 222
Bessel's equation 3 202
Bessel's equation, boundary problems for 312
Bessel's inequality 56
Bessel's integral 218
beta function 258 369—370
Beta function, incomplete 99
Binomial distribution 121
Boas, M.L. xviii
Bohr — Sommerfeld condition 250
Bound state 65
Boundary value problems 299
Boundary value problems for Bessel's equation 312
Canonical form 253 395
Central field 244 318
Charlier polynomials 117
Charlier polynomials, analogs 167 174
Charlier polynomials, tables 180 182—185
Chebyshev polynomials 22 35 393
Chebyshev polynomials, zeros of 355
Chebyshev, P.L. xvi
Christoffel numbers 354 359—362
Classical orthogonal polynomials xiii xvi 30 395
Classical orthogonal polynomials as eigenfunctions 67
Classical orthogonal polynomials as hypergeometric functions 282
Classical orthogonal polynomials asymptotic formulas 242
Classical orthogonal polynomials data (table) 32
Classical orthogonal polynomials inequalities 47
Classical orthogonal polynomials of discrete variable 108 113 139 399
Classical orthogonal polynomials of discrete variable on a lattice 142
Classical orthogonal polynomials of discrete variable on nonuniform lattices 146
Classical orthogonal polynomials qualitative properties 45
Classical orthogonal polynomials recursion formulas 38
Classical orthogonal polynomials solving eigenvalue problems 65
Classical orthogonal polynomials, series of 55
Classification of lattices 155
Classification of polynomial systems 157
Clebsch — Gordan coefficients xvi 341
Closed 56
Closure 57
Comparison theorems 305
Complete systems 56
Complete systems of eigenfunctions 301
Compression of information 363
Confluent hypergeometric equation 254 299
Confluent hypergeometric functions 258 411
Confluent hypergeometric functions, functional equations 271
Confluent hypergeometric functions, second kind 260
Convergence, uniform 61 212
Coulomb, C.A. de, field 317 320 326 330
Coulomb, C.A. de, potential xiii
Curvilinear coordinates 297
Cylinder functions xviii 202
d'Alembert's test 212
Darboux — Christoffel formula 39 197
Derivatives of polynomials of hypergeometric type 6
Derivatives, difference 142
Difference derivative 142
Difference equations 107
Difference equations of hypergeometric type 136
Difference formulas 122
Difference operators 107
Differential equation xv
Differential equation, fundamental 1
Differentiation formulas 18 25 98 393
Dini expansions 315
Dirac equation xiii 1 5 318
Dirac equation for Coulomb field 330
Dirichlet problem 89
Duplication formula 371
Eigenfunctions 66
Eigenfunctions of Sturm — Liouville problem 303 307
Eigenfunctions, infinity of 307
eigenvalue problems 65 302
Eigenvalues 66 300
Eigenvalues of Sturm — Liouville problem 303 307
EKG (electrocardiogram) 363—364
Electromagnetic waves xv 299
Elementary functions as hypergeometric functions 282
Elliptic integrals 289
energy levels 65
Equation of hypergeometric type 3 253
Equation, Bessel 3 202
Equation, Dirac xiii 1 5 318
Equation, Dirac, for Coulomb field 330
Equation, generalized, of hypergeometric type 253
Equation, Lommel 4 202 231 254 403
Equation, Parseval's 56
Equiconvergence 64
Error function 99 103 402—403
Euler angles 85—86
Euler's constant 101 375
Expansions in eigenfunctions 311
Expansions of functions 55 59
Expansions of plane and spherical waves 234 407
Expansions of polynomials 33
Expansions, Dini, Fourier — Bessel 315
Exponential integrals 101 401
Finite-difference analogs 108
Fourier coefficients, series 56
Fourier integral 64
Fourier — Bessel expansions 315
Fourier — Bessel integral 315 406
Fresnel integrals 103 403
Functional equations 370
Functions expansions in series 55
Functions integral representations 9
Functions of hypergeometric type 9 21
Functions of hypergeometric type in definite integrals 291
| Functions of second kind 96
Functions of second kind as hypergeometric functions 286
g-analogs 161
g-gamma functions 163
Gamma function 22 258 369—380 387—389
Gamma function, graph 374
Gamma function, incomplete 99
Gamma function, logarithmic derivative 374
Gamma function, poles 373
Gauss's equation 254
Gaussian quadratures 353
Gegenbauer polynomials 393
Gegenbauer's addition theorem 228—234 406
Generalized equation of hypergeometric type 253 389
Generalized equation of hypergeometric type, canonical form 253
Generating functions 26
Generating functions, Hermite polynomials 29
Generating functions, Laguerre polynomials 29
Generating functions, Legendre polynomials 28
Generating functions, polynomials of hypergeometric type 26
Graf's addition formula 227 406
Gram determinant 34
Hahn polynomials xvii 117
Hahn polynomials analogs 167 171 174
Hahn polynomials and Clebsch — Gordan coefficients 341
Hahn polynomials tables 180—186 196
Hankel functions 202
Hankel functions first and second kind 205
Hankel functions graphs 221
Hankel functions Sommerfeld representations 215
harmonic oscillator 71 250 317
Harmonic polynomials 83
Harmonics, spherical 76
Heat conduction xv
Helmholtz equation 1 201 220 297
Hermite equation 254 256 299
Hermite functions 261 273 413—414
Hermite functions, second kind 100 103
Hermite polynomials 21 72 393;
Hermite polynomials generating function 29
Hermite polynomials maxima 47
Hydrogen-like atoms 320
Hyperbolic functions 73
Hypergeometric equation 254
Hypergeometric equation table of solutions 281
Hypergeometric functions xii 253 409
Hypergeometric functions, functional equations 269
Hypergeometric functions, recursions 261
Hypergeometric type xvi
Hypergeometric type, equation of xvi 390
Hypergeometric type, functions of xvi 265
Hypergeometric type, functions of, difference equations 108 137 146
Hypergeometric type, functions of, power series 267
Hypergeometric type, polynomials of 6
Incomplete beta and gamma functions 99 401
Inequalities for classical orthogonal polynomials 47
Inequalities, Bessel's 56
Inequalities, Cauchy — Bunyakovsky 52
Inequalities, Schwarz 52
Infinity of solutions 307
Information, compression of 363
Integral cosine, sine 102 402
Integral representations for derivatives 17
Integral representations for derivatives, functions of hypergeometric type 9
Integral representations for derivatives, functions of second kind 96
Integral representations for derivatives, orthogonal polynomials of a discrete variable 139
Integrals, analytic 13
Integrals, containing functions of hypergeometric type 291
Integrals, Fourier 64
Integrals, Fourier — Bessel 315 406
Integrals, Fresnel 103 403
Integrals, Sonine — Gegenbauer 292
Integration formulas 353
Jacobi polynomials 21 393;
Klein — Gordon equation xiii 1 318
Klein — Gordon equation central field 326
Kravchuk polynomials 117 134
Kravchuk polynomials analogs 167 172
Kravchuk polynomials tables 180—185
l'Hospital's rule 70 213 278
Laguerre function, second kind 100
Laguerre polynomials 21 393;
Laguerre polynomials generating function 28 29
Laguerre polynomials graphs 47
Laguerre polynomials in Dirac equation 335—340
Laguerre polynomials maxima 47
Langer, R.E. 235 246
Laplace equation 1 76 89
Laplace integral 380
Laplacian 297
Laser sounding 364
Lattices classification 155
Lattices construction 197
Lattices quadratic 157 161
Legendre functions, associated 79
Legendre polynomials 22 28 46 393 396
Legendre polynomials graphs, maxima 46
Legendre polynomials, associated 99
Leibniz's rule 25 94
Lidar 365
Light, absorption of 357
Liouville, J. elementary Bessel functions 222
Logarithmic derivative 276 374 389
Lommel equation 4 202 231 254 403
MacDonald's function 223 293
Macdonald's function graph 225
Mean square deviation 55
Meixner polynomials 117
Meixner polynomials analogs 167 172
Meixner polynomials tables 180—185
Modified Bessel functions 223 407
Modified Bessel functions application 364
Modified Bessel functions graphs 225
Molecular spectra 317—318
Moments 34
Multipole expansion 89
Neumann functions 219
Neutrons 317
Nonhomogeneous differential equation 301
Nonuniform lattices 142
Nuclear reactors xiii
Numerical analysis 353 (§27)
Numerical analysis integration 353 358
Numerical analysis summation 357
Orthogonal polynomials 29 394
Orthogonal polynomials Darboux — Christoffel formula 39
Orthogonal polynomials moments 34
Orthogonal polynomials parity 40
Orthogonal polynomials zeros 39
Orthogonal polynomials, classical xiii xvi 30 32 395
Orthogonal polynomials, classical, Darboux — Christoffel formula 39
Orthogonal polynomials, classical, derivatives of 30
Orthogonal polynomials, classical, general properties 33
Orthogonal polynomials, classical, of discrete variable xi xv xvi 108 128
Orthogonal polynomials, classical, of discrete variable as hypergeometric functions 284
Orthogonal polynomials, classical, of discrete variable in summation 356
Orthogonal polynomials, classical, of discrete variable, limit properties 132
Orthogonal polynomials, classical, of discrete variable, q-analogs 161
Orthogonal polynomials, classical, of discrete variable, second kind 140
Orthogonality 29
Orthogonality of eigenfunctions 303 313
Orthogonality of polynomials of a discrete variable 113 124
Orthogonality of polynomials on nonuniform lattice 152 157
Oscillation 304
Parabolic coordinates 297
Parabolic cylinder coordinates 297
Parabolic cylinder functions 414
Parseval's equation 56
Pascal distribution 121
Poeschl — Teller potential 73
|
|
|
| Реклама |
|
|
|
|
|
О проекте