Mathematical Physics Vol 1

482

INDEX

normalized, 264 orthonormal, 264

of the second kind, 245 exponential, 254 Fourier, 307, 322, 323 Fresnel, 254 in the Riemannian sense, 48 line, 48, 50 Newton’s relation, 48 Poisson, 377

Gamma function, 245 Gauss-Legendre multiplication formula, 251 Gaussian hypergeometric function, 260 general integral, 342, 351 general solution, 342, 350–352, 385 generalized binomial coefficients, 250 generalized coordinates, 108, 113 geometric interpretation

integral sum, 48, 50 integral surfaces, 342 integration factor, 347 involution, 353, 354 Jacobi elliptic function, 259 Jacobian, 200, 357 Kronecker’s symbol, 24 Lagrange-Charpit method, 352 Lamé coefficients, 110, 114 Laplace equation, 104, 371 Laplace operator, 88 Laplacian, 88, 113 law parallelogram, 17 Legendre formula, 251 Legendre function, 228 Legendre integrals, 258 Legendre polynomials, 271

of a mixed product, 63 of vector product, 62

GL-differintegral, 444 Grünwald-Letnikoff

Left-sided Derivative, 459 Right-sided Derivative, 459

gradient, 80, 84, 86, 113 of a function, 86, 87

of a scalar function, 86 partial, 86 projection, 84

Green formula first, 371

second, 371 Green formulas, 370 Green function, 379 Grunwald-Letnikov derivative left, 444

limit value, 40 line integral, 50 linear operator addition, 35

harmonic, 308 sum, 309

superposition, 309 harmonic function, 104, 371 Hermit polynomials, 243 hodograph, 40, 43 pole, 40

components, 35 multiplication by a scalar, 35

linear vector space, 32 Liouville-Weyl fractional derivatives left, 446 right, 446 Liouville-Weyl fractional integrals, 447 mathematical pendulum, 297 Mayer bracket, 353 mean square error, 318 memory length, 444 method Fourier, 364 Lagrange-Charpit, 352 of variable separation, 364 metric tensor, 113 Miller-Ross function, 256

identity operator, 447 increment geometric, 41

of the argument, 41

indefinite integral

of a vector function, 47 vector function, 47

inequality

Bessel, 319

integral

Euler

of the first kind, 251