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| Авторизация |
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| Morse P.M. — Methods of theoretical physics |
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| Предметный указатель |
Integral representation for solutions, of differential equations, and separated wave equation 637
Integral representation for solutions, of differential equations, for Bessel functions 619 620
Integral representation for solutions, of differential equations, for Bessel functions, spherical 622
Integral representation for solutions, of differential equations, for Hankel functions 623—624
Integral representation for solutions, of differential equations, for hypergeometric function 579 588 592 593 669
Integral representation for solutions, of differential equations, for hypergeometric function, confluent 605 672
Integral representation for solutions, of differential equations, for Mathieu functions 633
Integral representation for solutions, of differential equations, for spheroidal functions 1505
Integral representation for solutions, of differential equations, kernel for 582
Integral representation for solutions, of differential equations, Legendre function 595 597
Integral representation for solutions, of differential equations, modulation factor for 582
Integral representation for solutions, of differential equations, table 669 672
Integral representation for solutions, of Laplace equation, and Legendre functions 1275
Integral representation for solutions, of Laplace equation, in coordinates, circular cylinder 1262
Integral representation for solutions, of Laplace equation, in coordinates, parabolic 1297
Integral representation for solutions, of Laplace equation, in coordinates, spherical 1270
Integral representation for solutions, of Laplace equation, in coordinates, spheroidal, oblate 1295
Integral representation for solutions, of Laplace equation, in coordinates, spheroidal, prolate 1288
Integral representation for solutions, of vector wave equation 1865
Integral representation for solutions, of wave equation 148
Integral representation for solutions, of wave equation, in spherical coordinates 1467
Integral representation for solutions, of wave equation, in spheroidal coordinates 1505
Integral, net circulation 18
Integral, net outflow 16 34
Integrals, evaluation by calculus of residues 408
Integrals, involving branch points 410 472
Integrals, surface 16
Integration factor and adjoints 527
Integration in complex plane 362
Integration in complex plane, and calculus of residues 408
Integration in complex plane, and Cauchy’s integral formula 367
Integration in complex plane, and Cauchy’s theorem 363
Intensity, field see Field intensity
Intensity, of sound wave 1374
Internal heating, transient, of slab 1590
Invariance 4 37 46 55 95
Invariance, gauge 207 210—212 1875
Invariance, in classical mechanics 290
Invariance, Lorentz see Lorentz invariance
Inverse function 361
Inverse function, inversion of series 411
Inverse operator, uniqueness of 1110
Inverse-cube law of force in quantum mechanics 1665
Inversion formula, Fourier 453
Inversion formula, Laplace 468
Inversion, and parity 1723
Inversion, in conformal mapping 451
Inversion, in conformal mapping, and inversion circle 452
Inversion, in conformal mapping, with respect to sphere 1317
Inversion, of series 411
Iris in duct, approximations for 1517
Iris in duct, approximations for, of circular cross section 1514
Iris in duct, approximations for, rectangular cross section 1443
Iris in duct, integral equation for 1516
Iris in duct, transmission factor 1515
Iris in duct, variational principle for 1516
Irregular singular point 534
Irregular singular point, equation with one 537
Irregular singular point, equation with one, and one regular 550
Irregular singular point, equation with one, and two regular 555
Irrotational fields 18
Irrotational flow 153 (see also Fluid flow; Incompressible fluid flow)
Isosceles right-triangle membrane 756
Isotimic surfaces 5
Isotropic elastic media 322 345
Isotropic scattering, integral equation for distribution function 1617
Iterate 1138
Iterated kernels 915
Iteration-perturbation (I — P) method 1001—1010
Iteration-perturbation (I — P) method, and variational method 1119
Iteration-perturbation (I — P) method, convergence of 1005 1020 1026
Iteration-perturbation (I — P) method, for Mathieu equation 1008
Iteration-perturbation (I — P) method, for scattering see Born approximation
Iteration-perturbation (I — P) method, in abstract vector space 1018
Iteration-perturbation (I — P) method, modified 1033
Iteration-perturbation (I — P) method, tabulation of formulas 1162
Iteration-perturbation (I — P) method, with nonorthogonal functions 1035
Iterations, method of minimized 1155
Iterations, three-term recursion formula for 1157
Jacobi elliptic functions 429
Jacobi polynomials 780
Jacobi polynomials, and two-particle Schroedinger equation 1731
Jacobi polynomials, normalization 781
Jacobi polynomials, recurrence formula 781 1755
Jacobi polynomials, table of formulas 1754
Joining formula 577
Joining formula, for associated Legendre functions 602
Joining formula, for confluent hypergeometric function 608
Joining formula, for Gegenbauer functions 602
Joining formula, for hypergeometric function 546 581 590 670
Kernels, for integral representations 582
Kernels, for integral representations, and Euler transform 585
Kernels, for integral representations, and functions of  644
Kernels, for integral representations, and Laplace transform 584
Kernels, for integral representations, and solutions of wave equation 636—638
Kernels, of integral equations 905 912
Kernels, of integral equations, classification of 951—956
Kernels, of integral equations, definite 909 910 912
Kernels, of integral equations, definite, negative 905 909
Kernels, of integral equations, definite, positive 905 909
Kernels, of integral equations, factorable 956
Kernels, of integral equations, indefinite 905 916
Kernels, of integral equations, iterated 915
Kernels, of integral equations, of form,  969
Kernels, of integral equations, of form,  936 960 962 996
Kernels, of integral equations, of form, , and faltung theorem 964
Kernels, of integral equations, of form, , and Fourier transforms 960 963—972
Kernels, of integral equations, of form, , and Laplace transform 972—975
Kernels, of integral equations, of form, , and Wiener — Hopf method 978—992
Kernels, of integral equations, of form,  976
Kernels, of integral equations, polar 905 909 911
Kernels, of integral equations, reciprocal 915
Kernels, of integral equations, semidefinite 909 916
Kernels, of integral equations, semidiagonal 952
Kernels, of integral equations, singular 921
Kernels, of integral equations, singular, intrinsically 924
Kernels, of integral equations, solving 914
Kernels, of integral equations, symmetric 908 912
Kernels, of integral equations, table of types 992
Kinetic energy, average 175
Kinetic energy, average, in fluid flow 307
Kinetic energy, average, of string 126
Kinetic potential 280
Kirchhoff approximation 1073
Kirchhoff approximation, convergence of 1074
Klein — Gordon equation 138 316 1343
Klein — Gordon equation, and Proca equation 221
Klein — Gordon equation, and relativistic quantum theory 256
Klein — Gordon equation, density for, canonical momentum 317
Klein — Gordon equation, density for, current and charge 318
Klein — Gordon equation, density for, field momentum 317
Klein — Gordon equation, density for, Lagrange 316
Klein — Gordon equation, dispersion and 140
Klein — Gordon equation, Green’s function for 139 854 1343
Klein — Gordon equation, Hamiltonian 317
Klein — Gordon equation, impulse function for 1343
Klein — Gordon equation, reciprocity principle for 854
Klystron electromagnetic resonator 1859
Klystron electromagnetic resonator, effective impedance of 1862
Klystron electromagnetic resonator, resonance frequencies of 1862
Knife edge, Fresnel diffraction by 1386 1406
Kronecker delta function 23
Lagrange density 276 318
Lagrange density, and Euler equation 277 342
Lagrange density, and invariance 338
Lagrange density, and variational integral 276 341
Lagrange density, for diffusion equation 313 344
Lagrange density, for Dirac equation 335 346
Lagrange density, for elastic media, anisotropic 325 345
Lagrange density, for elastic media, isotropic 322 345
| Lagrange density, for electromagnetic field 327 346
Lagrange density, for fluid flow 307 343
Lagrange density, for Klein — Gordon equation 316 344
Lagrange density, for Laplace equation 307
Lagrange density, for Schroedinger equation 314
Lagrange density, for string 303 343
Lagrange density, for vector fields 318
Lagrange density, for wave equation 304 308 343
Lagrange density, table 341—346
Lagrange function 229 280
Lagrange function, and conjugate momenta 229
Lagrange function, and conjugate variables 229
Lagrange function, and Hamilton’s principle 280
Lagrange function, and Lagrange equation of motion 281
Lagrange function, and momentum 281
Lagrange function, for charged particle 294
Lagrange function, for dissipative systems 298
Lagrange function, for relativistic particle 297
Lagrange multipliers 278
Lagrange — Euler equation 276—280 318 342
Laguerre polynomials 784
Laguerre polynomials, and coulomb potential 1664 1668
Laguerre polynomials, and integral equations 937
Laguerre polynomials, and three-dimensional oscillator 1662
Laguerre polynomials, associated 784
Laguerre polynomials, factorization method and 789
Laguerre polynomials, integral equation for 904
Laguerre polynomials, table of properties 784
Lame equation 648
Lame equation, and ellipsoidal harmonics 1306
Lame equation, and Laplace equation 1305
Laplace equation 7 1173—1330
Laplace equation, and Bessel functions 1259
Laplace equation, and bipolar coordinates 1210
Laplace equation, and complex variables 1215 1252
Laplace equation, and conformal mapping 1175 1216 1243—1252
Laplace equation, and hyperbolic coordinates 1209
Laplace equation, and incompressible fluid flow 155
Laplace equation, and Neumann boundary conditions 703
Laplace equation, cartesian coordinates and see Cartesian coordinates
Laplace equation, difference equation for 695
Laplace equation, Dirichlet boundary conditions for 703
Laplace equation, Green s function for see Green’s function
Laplace equation, in bispherical coordinates 523 1298
Laplace equation, in cartesian coordinates 709 1175 1256
Laplace equation, in circular cylinder coordinates 1259
Laplace equation, in ellipsoidal coordinates 1304
Laplace equation, in elliptic coordinates 1195
Laplace equation, in parabolic coordinates 1207 1296
Laplace equation, in polar coordinates 1183
Laplace equation, in spherical coordinates see Spherical coordinates
Laplace equation, in spheroidal coordinates, oblate 1292
Laplace equation, in spheroidal coordinates, prolate 1284
Laplace equation, in three dimensions 1252—1309
Laplace equation, in toroidal coordinates 522 1301
Laplace equation, in two dimensions 1175—1252
Laplace equation, Lagrange density for 307
Laplace equation, maxima and minima 7 703
Laplace equation, separability of, in three dimensions 518
Laplace equation, separability of, in three dimensions, and confocal cyclides 519
Laplace equation, separability of, in three dimensions, and modulation factor 518
Laplace equation, separability of, in two dimensions 499
Laplace equation, separability of, in two dimensions, and conformal mapping 499
Laplace equation, variational method for 1108
Laplace equation, vector see Vector Laplace equation
Laplace equation, viscous flow 1185
Laplace transform 467
Laplace transform, and diffusion 1596—1602
Laplace transform, and distribution function 1624
Laplace transform, and forced vibration 1339
Laplace transform, and integral equations 944 994
Laplace transform, and nonorthogonal eigenfunctions 1348
Laplace transform, and Volterra equation 972 (see also Fourier transform)
Laplace transform, as kernel for integral representations 584 605
Laplace transform, as kernel for integral representations, and confluent hypergeometric equation 605
Laplace transform, as kernel for integral representations, and Mathieu functions 634
Laplace transform, faltung theorem for 468 484
Laplace transform, inversion formula for 468
Laplace transform, table 1579
Laplace transform, table, of properties 484
Laplacian 6
Laplacian, in curvilinear coordinates 115—117 338
Laplacian, of vector, in curvilinear coordinates 115—117
Laplacian, of vector, in tensor notation 51
Laurent series 378
Laurent series, and isolated singularities 380
Laurent series, and multipoles in electrostatics 379
Legendre equation 594
Legendre equation, solution, of first kind 545 595
Legendre equation, solution, of second kind 545 597
Legendre equation, Wronskian 599
Legendre functions 545
Legendre functions, addition theorem for 1274
Legendre functions, and harmonics 1264
Legendre functions, and Laplace equation 1264
Legendre functions, and Legendre functions of second kind 599
Legendre functions, and Legendre polynomials 597
Legendre functions, and multipoles 1276
Legendre functions, as hypergeometric function 595
Legendre functions, associated 548
Legendre functions, associated, addition formula for 784
Legendre functions, associated, and Ferrer’s spherical harmonic 1286
Legendre functions, associated, and finiteness boundary condition 715
Legendre functions, associated, and Gegenbauer functions 782
Legendre functions, associated, and Hobson’s spherical harmonic 1286
Legendre functions, associated, and hypergeometric function 601
Legendre functions, associated, and Laplace equation, in bispherical coordinates 1299
Legendre functions, associated, and Laplace equation, in spherical coordinates 1264
Legendre functions, associated, and Laplace equation, in spheroidal coordinates, oblate 1292
Legendre functions, associated, and Laplace equation, in spheroidal coordinates, prolate 1285
Legendre functions, associated, and second solution 603
Legendre functions, associated, and tesseral polynomials 549
Legendre functions, associated, and Tschebyscheff polynomials 604
Legendre functions, associated, density function for 782
Legendre functions, associated, derivative formula for 601
Legendre functions, associated, eigenvalues and 733
Legendre functions, associated, factorization of equation for 731 734 789
Legendre functions, associated, joining fomula for 602
Legendre functions, associated, normalization of 783
Legendre functions, associated, of half-integral order 1302
Legendre functions, associated, polynomials for 601
Legendre functions, associated, recurrence formulas 735 782
Legendre functions, associated, table, of formulas 1325—1330
Legendre functions, associated, table, of values 783
Legendre functions, asymptotic behavior 596
Legendre functions, generalized 548
Legendre functions, integral representation for 595 596 1275
Legendre functions, of imaginary argument 1292 1328
Legendre functions, of second kind 545 652
Legendre functions, of second kind, and hypergeometric function 598
Legendre functions, of second kind, and Legendre functions 599
Legendre functions, of second kind, and Legendre polynomials 752
Legendre functions, of second kind, asymptotic behavior of 598
Legendre functions, of second kind, generating function for 753
Legendre functions, of second kind, integral representation of 597
Legendre functions, of second kind, recurrence relations for 600
Legendre functions, of second kind, table, of formulas 1327—1328
Legendre functions, of second kind, table, of values 1921—1923
Legendre functions, of second kind, Wronskian for 599
Legendre functions, recurrence relations 600
Legendre functions, table of formulas 1325—1330
Legendre functions, tables of values of 1920—1922 1927
Legendre functions, Wronskian 599
Legendre polynomials 549 748
Legendre polynomials, and Gegenbauer polynomials 782
Legendre polynomials, and Legendre functions of second kind 752
Legendre polynomials, and orthogonalization of powers 780
Legendre polynomials, completeness of 572
Legendre polynomials, derivative formula for 601
Legendre polynomials, formula for 750 751
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