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| Morse P., Feshbach H. — Methods of Theoretical Physics (part 1) |
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| Предметный указатель |
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 table of properties 992—996
Integral variational principle for 912 914 1120
Integral Volterra 905 920 972
Integral Wiener — Hopf method for 978—992
Integrals involving branch points 410 472
Integrals surface 16
Integrals, evaluation by calculus of residues 408
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 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
Inverse function 361
Inverse function inversion of series 411
Inverse operator, uniqueness of 1110
Inverse-cube law of force in quantum mechanics 1665
Inversion and parity 1723
Inversion formula Fourier 453
Inversion formula Laplace 468
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 classification of 951—956
Kernels definite 909 910 912
Kernels definite negative 905 909
Kernels definite positive 905 909
Kernels for integral representations 582
Kernels for integral representations and Euler transform 585
Kernels for integral representations and functions of zt 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 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 in fluid flow 307
Kinetic energy 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 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, Lagrange density for 307
Laplace equation, maxima and minima 7 703
Laplace equation, variational method for 1108
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 eigenf unctions 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 density function for 782
Legendre functions associated derivative formula for 601
Legendre functions associated eigenvalues and 733
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, associated and Ferrer’s spherical harmonic 1286
Legendre functions, associated and fmiteness 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 factorization of equation for 731 734 789
Legendre functions, associated joining formula 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, 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
Legendre polynomials generating function for 597 748
Legendre polynomials integral equation for 903
Legendre polynomials normalization 751
Legendre polynomials powers, expansion in 750
Legendre polynomials recurrence formulas 749 782
Legendre polynomials spheroidal function, expansion of, in 573 1503
Legendre polynomials tables of formulas 783 1326—1327
Legendre polynomials values, special 750
Levels, virtual 1074 1658 1686
Lift 1228—1231
Lift and analytic functions 1228
Lift and circulation about circular cylinder 1228
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