Mathematical Physics Vol 1

484

INDEX

orthogonal, 108 point, 20

power, 223, 225, 227 operations, 225 trigonometric, 307, 310 uniformly convergent, 224, 310 properties, 224

quadratic form, 362

Rabotnov function, 256, 441 radius convergence, 225 of curvature, 73 of torsion, 73 reduction formula, 245, 249 Reflection theorem, 250 regular singular point, 232 residue, 251 Riemann theorem, 320 Riemann-Liouville

set

orthonormal, 23 sine integral, 254 singular point, 231 singular points, 344 singular solution, 342, 350, 351 solenoid, 90 solution fundamental, 242 space affine, 23 Euclidean, 23, 108 metric, 33 real vector, 23 vector, 27 spherical pendulum, 300 Stirling formula, 251

Left-sided Derivative, 459 Left-sided Integral, 459 Right-sided Derivative, 459 Right-sided Integral, 459 Riemann-Liouville fractional derivative left, 442 Riemann-Liouville fractional integral left, 442 Riemann-Liouville fractional derivative right, 442 Riemann-Liouville fractional integral right, 442

Sturm – Liouville task, 366 Sturm – Liouville theory, 365 Sturm–Liouville problem, 266, 268, 288 superposition, 356 of harmonics, 309 superposition principle application, 367 surface equiscalar, 80 nonorientable, 51 one-sided, 51 surface integral vector, 53 symbol delta, 112 Kronecker, 112 symmetrical form, 344 tangent, 73, 83 tautochrone problem, 436 tensor, 13 theorem Abel’s, 225 Helmholtz’s, 108 on convergence of Fourier, 311 on convergence of Fourier series, 311 on mean value, 102 Riemann, 320

rigid body, 17 rotor, 113, 349 scalar, 13 scalar function

partial gradient, 86 scalar potential, 108 scalar product, 22, 23 series

absolutely convergent, 224 convergent, 224 divergent, 224 Fourier, 307, 310, 311

complex form, 321 convergence, 311 generalized, 265 of even and odd functions, 312 on the interval ( − π , π ) , 315 on the interval ( 0 ,ℓ ) , 315 sine and cosine, 312, 313 functional, 223 of orthogonal functions, 265