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| Sommerfeld A. — Partial Differential Equations in Physics |
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| Предметный указатель |
Abraham, M. 223 244 256
Absorption condition 190
Addition theorem, of Bessel and Hankel functions 107 234
Addition theorem, of spherical harmonios 133
Addition theorem, of the preceding and the standing wave 146
Adjoint, differential form 44
Airy integrals 118 123 149
Alkali atoms 206
Anharmonic analysis 27
Anharmonic analysis, normalization condition of 293
Antenna 239
Antenna, frame 245 267
Antenna, horizontal 243
Antenna, magnetic see "Frame"
Antenna, vertical 242
Approximation at a point of discontinuity 12
Approximation at a point of discontinuity, oscillating 17 26
Approximation at a point of discontinuity, osculating 17 26
Associated spherical harmonics 126
Associated spherical harmonics, normalization of 132
Associated spherical harmonics, recursion formula for 132
Associated spherical harmonics, with negative index m 128
Asymptotic representation, of Hankel functions 100 119
Asymptotic representation, of Hankel functions, of spherical harmonics 146
Balmer term 200 204
Bauer, G. 235
Baule, B. 37
Bending of beams 303
Bessel functions 84
Bessel functions, generating function 107
Bessel functions, integral representation of 86
Bessel functions, integral representation of functions in terms of 109
Bessel functions, summation over the roots of 295
Bessel functions, with fractional indices 111
Bipole 151
Bohr, N. 201
Boundary condition, adiabatic 63
Boundary condition, adiabatic, homogeneous, inhomogeneous 82 177
Boundary condition, adiabatic, isothermal 63
Boundary condition, adiabatic, of exterior heat conduction 64
Boundary value problems, general, in acoustics and heat conduction 177 180
Boundary value problems, general, in acoustics and heat conduction, exterior, of the wave equation 214
Boundary value problems, general, in acoustics and heat conduction, in the potential equation 181
Boundary value problems, general, in acoustics and heat conduction, of the first and second kind 53
Bush and Caldwell 4
Caratheodory, C. 320
Characteristics, theory of 36
Charge cloud 205
Christoffbl, E.B. 159
Circuit relations for  and  293
Circuit relations for and , semi 251 253
Completeness relation 5
Confluent hypergeometric function 154
Couette flow 292
Courant — Hilbert 172 179
Cylinder function, general 86
Cylinder problems of heat conduction 101
Cylindrical wave 100 108
D'Alembert's solution of the wave equation 41
Darwin, C.G. 129
de Broglie, L. 207
de l'Hospital's rule 93
Debye, P., asymptotic representation of the Hankel functions 119
Debye, saddel point method of 116 118
Delta function 3 27 58 72
Diffusion 33
Diffusion, coefficient 34
Diffusion, Fick's law 34
Dipole, Hertz 151 236
Dipole, Hertz, magentic 268
Dirac, P.A.M. 27 183
Direction characteristic of the horizontal antenna 261
Dirichlet, discontinuous factor 290 299
Dirichlet, discontinuous factor, problem of potential theory 130 186
Dispersion by colloidal particles 224
Drop lines 99
Earth absorption in radio 271
Earth's temperature 68
Eigen value spectrum, continuous and discontinuous 188
Eigen Values 466
Eigen values, continuous spectrum 188 193
Eigen values, degenerate case 167
Eigen values, in wave mechanics 200
Eigen values, of the hydrogen atom 204 225
Eigen-differentials 211
Eigenfunctions 166
Eigenfunctions, conjugate complex 186
Eigenfunctions, improper and proper 221
Eigenfunctions, of the hydrogen atom 204 225
Eigenfunctions, regular and singular 221
Elastic rod 33 291
Electrodynamics of variable fields, differential equation of 32
Elliptic differential equations 38 42
Epstein, P. 255
Error, mean square 2 22
Euler's constant 94
Faber, G. 99
Fluid friction 33
Fourier analysis, anharmonic 27 77
Fourier analysis, anharmonic, analysis of crystals 20
Fourier analysis, anharmonic, integral 19 59
Fourier analysis, anharmonic, representation of coefficients 3
Fourier analysis, anharmonic, transformation 21
Fourier series 1
Fourier series, convergence of 14
Fourier, J.B. 1 92 101
Frank-mises 80 192 236
Fredholm — Hilbert theory of integral equations 169
Freedom, degrees of, infinite number for oscillating systems 169
Frequency  20 84
Function space 180
Fundamental state of the H atom 205
Fundamental theorem of the theory of oscillating systems with an infinite number of degrees of freedom 178
Gauss, C.F. 1 94 153 171
Gauss, law of error 59
Gauss, law of error, series 153
Gauss, theorem of the arithmetic mean in potential theory 181 295
Gegenbauer polynomials 227 229
Generating function, of the Bessel functions of integral index 107
Generating function, of the Bessel functions of integral index, of spherical harmonics 123
Gibbs' phenomenon 12
Gibbs, W. 12
Gordon, W. 200
Gratiatos, J. 289
Green's function for self-adjoint differential equations 49 61 198
Green's function for self-adjoint differential equations, as the solution of an integral equation 183
Green's function for self-adjoint differential equations, for a continuous spectrum 193
Green's function for self-adjoint differential equations, for the wave equation 182
Green's function for self-adjoint differential equations, for the wave equation in the exterior of a sphere 198
Green's function for self-adjoint differential equations, in many-dimensional space 232
Green's function for self-adjoint differential equations, of the sphere in potential theory 134
Green's function for self-adjoint differential equations, one dimensional 291
Green's function for self-adjoint differential equations, reciprocity of the 50 217
Green's theorem 45
Green's theorem, for linear heat conduction 55
Green's theorem, the second form of 291
Hankel functions, integral representation of 88
Hankel functions, integral representation of, asymptotic representation 98 294
Hankel functions, integral representation of, logarithmic singularity of  294
Hankel functions, integral representation of, with fractional index 113
Hankel, symbol 117
Harmonic analyzer 4
Heat conduction, linear 35
Heat conductivity 34
Heat conductivity, ratio of outer and inner 293
Heat conductivity, ratio with electric conductivity 293
Heat equation 34
Heisenberg, W. 201
Hermite polynomials 27 302
Hertz, concave mirror experiment 162
| Hertz, concave mirror experiment, dipole 236 237
Hertz, concave mirror experiment, force line diagrams for the oscillating dipole 244
Hertz, concave mirror experiment, vector 238
Hertz, H. 236 244 276
Hilbert space 179 184
Hilbert, D. 166
Hobson, E.W. 129
Hydrogen eigenfunctions 204 225
Hydrogen radius 205
Hyperbolic differential equation 38 41
Hypergeometric function, differential equation of the 152
Hypergeometric function, differential equation of the, confluent 154
Image, electric 135
Integral equations, Hilbert's theory of 169 184
Integral equations, Hilbert's theory of, orthogonality theorem 188
Integral sine 11
Integration, complex 290
inversion 136
Inversion, center of 139
Inversion, sphere of 139
Ionosphere (Kenelly — Heaviside layer) 236
Jacobi, C.G.J. 72
Kepler problem for the H atom 201
Kernel, resolving 50
Kernel, resolving, symmetric 184
Laguerre, differential equation 204
Laguerre, differential equation, polynomials 27 205 302
Lame wave function 224
Lame, G. 81
Laplace operator 32
Laplace, P.S. 131
Laurent series 109
Legendre polynomials 129
Leibniz series 12
Liouville theorem on conformal mapping 140
Lyman series 204
Magnus — Oberhettinger 235
Many dimensional space, spherical wave and Green's, function in 232
Mapping, con formal through reciprocal radii 139
Marconi, G. 262
Mathieu equation 168
Maxwell, J.C. 130 135 152 247
Meander line 7
Measurement, general electrodynamic system of 237
Membrane, vibrating 166
Method of least squares 22
Mie, G., dispersion by colloidal particles 224
Misdirection and correct direction in range finding 267
Monge, theory of characteristics 37
Mott and Massey 209
Multipole, electric 149 see "Bipole" "Quadrupole" "Octupole"
Murray, F.H. 257
Navier — Stokes equation 34 292
Neumann function 90
Neumann, C. and F. 158
Newtonian potential 49 123
Nicholson, J.W. 122
Niessen, K.F. 257
Nodal lines of the vibrating membrane 170 174
Non-uniform convergence of the approximation process 12
Normal coordinates 169
Normalization of the eigenfunction in the infinite domain 210
Normalizing condition 3
Numerical distance 256
Octupole 151
Ohm G.S. 179
Ohm — Rayleigh principle 179
Ohm's law 34
Orthogonality condition 2 22 124
Oscillating membrane 33 166
Oscillating membrane, string 33
Oscillations, Free and forced 182
Ott, H. 256
Parabolic coordinates in the wave mechanical scattering problem 225
Parabolic differential equations 38 43
Partial differential equation of the second order, most general form of a linear 36
pass method 99
Perturbation theory in wave mechanics 170 188
Pipe, open and covered 291
Plane wave 84
Plate, flow, laminar, of an incompressible viscous fluid 291
Poincare, fundamental theorem of the theory of eigenfunctions 168
Poincare, fundamental theorem of the theory of eigenfunctions, domain of validity of asymptotic series 117
Poissons's equation 182
Poissons's equation, integral 138
Potential equation, in hydrodynamics 32
Potential theory, Dirichlet problem 130 186
Potential theory, Dirichlet problem Green's function for a sphere 134
Potential theory, Dirichlet problem one dimensional 291
Probability concept in wave mechanics 201 205
Quadrupole 151
Quantum number, azimuthal, radial, principal, nagnetic 202 203
Radiation condition 189
Radiation energy 270
Radio on a plane and spherical earth 236
Rainbow 224
Rainbow, Airy's theory 123
Rare gases as eight-shells 206
Rayleigh, theory of sound 179
Reciprocal radii 135
Reciprocity law 50 184
Reflection of the plane wave on the sphere 224
Relativity, special theory of, its differential equation 32
Rellich, F. 192
Renner, F. 275 277
Resonance catastrophe 187
Riemann's two-sheeted space 80
Riemann's two-sheeted space, integration of the hyperbolic differential equation 52
Riemann's two-sheeted space, problem of sound waves 164
Riemann, B. 109
Ring problem in heat conduction 71
Rutherford's model of the H atom 200 210
Rutherford's model of the H atom, formula of nuclear physics 206
Rydberg constant 201 204
s-term 206
Saddle point method 98
Saddle point method, according to Debye 116 118
Sauter, F. 192 215
Scattering, wave mechanical 206
Schlaefli 88
Schmidt, E. 184
Schoenflies, A. 81
Schroedinger, E. 166
Schroedinoer, equation 35 200
Self-adjointness, condition of 45
Semi-convergent 116
Series expansions in linear differential equations 92
Sommerfeld, A. 57 80 88 221 235
Sommerfeld, A., and Renner, F. 277
Spherical geometry 140
Spherical harmonics 123
Spherical harmonics, addition theorem of 133 146
Spherical harmonics, as special case of the hypergeometric differential equation 153
Spherical harmonics, asymptotic representation of 146
Spherical harmonics, development by 21
Spherical harmonics, difference equation 124
Spherical harmonics, differential equation of 123
Spherical harmonics, generating function of 123
Spherical harmonics, integral representation of 130
Spherical harmonics, Laplace integral of 131
Spherical harmonics, of non-integral index 155
Spherical harmonics, of the second kind 157
Spherical harmonics, of the second kind, generating function 158
Spherical harmonics, of the second kind, integral representation 158
Spherical harmonics, of the second kind, their singularity 157
Spherical harmonics, orthogonality and normalization con-dition 124
Spherical harmonics, zonal 127 131
Spherical wave 109 143
Stefan — Boltzmann law 64
Surface spherical harmonics 130
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