Mathematical Physics Vol 1

481

INDEX

elliptic modulus, 258 equation cylindrical, 234

fractional integral, 460 fractional Riemann-Liouville integral, 442

fractionul calculus, 455 Frobenius method, 232 function analytical, 226

heat conduction, 363 index, 233 Laplace, 363, 371

in cylindrical coordinates, 370 in spherical coordinates, 369 of elliptic type, 369 of the membrane, 339 Poisson, 371 Sturm–Liouville, 266 wave, 338, 341, 362, 426

approximation by a trigonometric poly nomial, 317 Bessel, 241, 242, 266, 274 of the first kind of zero order, 235 of the second kind of zero order, 237 of the second type of order n, 240 error, 253 complementary, 253 even properties, 313 factorial, 244 gamma, 238, 244 geometric increment, 43 gradient, 86 harmonic, 104, 371

equiscalar

line, 80 surface, 80 Euclidean space over a field, 23 Euler constant γ , 245 Euler gamma function, 248

Euler Psi function, 251 exponential integral, 254 factorial function, 244 field, 79, 103

Hermite, 275 Laguerre, 275 Legendre, 228 Macdonald, 237 Neumann

irrotational, 108 potenctial, 108 scalar, 79 stationary, 80

of zero order, 237

non-periodic

Finite-Difference

extension, 309 normalized, 263 normalized set, 264 odd properties, 313 orthogonal, 263, 265 orthonormal completeness, 265 orthonormal set, 264 partially continuous, 311 partially smooth, 311 periodic, 307 properties, 308 primitive, 47, 48 principal, 267 special, 243, 244 vector, 39 continuous, 41 domain, 39 Weber, 241, 242

Left-sided, 459 Right-sided, 459 first integral, 343, 344, 384, 385 force gravitational, 103 Newton’s, 105 formula Frenet-Serret, 73 Rodrigues, 231 formulas Green, 370 Fourier coefficients, 265 Fourier formula, 323 Fourier integral, 322, 323 Fourier method, 369

solving equations of hyperbolic type, 365 solving equations of parabolic type, 365

Fourier series

complex form, 321

fractional derivative

of a constant function, 436

function set