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Nikiforov A.F., Uvarov V. — Special Functions of Mathematical Physics: A Unified Introduction with Applications
Nikiforov A.F., Uvarov V. — Special Functions of Mathematical Physics: A Unified Introduction with Applications

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Название: Special Functions of Mathematical Physics: A Unified Introduction with Applications

Авторы: Nikiforov A.F., Uvarov V.

Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 427

Добавлена в каталог: 02.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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
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