Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 258
Gerald Goertzel, Nunzio Tralli. analytic within a closed contour C and continuous on the contour C. Then if a is any arbitrary point within C f ( a ) 1 f ( z ) 2πi Jc z a dz ( 1C.10 ) This relation is known as the Cauchy integral formula ...
Gerald Goertzel, Nunzio Tralli. analytic within a closed contour C and continuous on the contour C. Then if a is any arbitrary point within C f ( a ) 1 f ( z ) 2πi Jc z a dz ( 1C.10 ) This relation is known as the Cauchy integral formula ...
Página 263
... contour C and the sign is plus if the contour is described in the counterclockwise direction and minus if in the clockwise direction . As an example , let us evaluate +00 eixt I1 - 2 dx + a2 ( 2A.4 ) We note that the integrand has poles ...
... contour C and the sign is plus if the contour is described in the counterclockwise direction and minus if in the clockwise direction . As an example , let us evaluate +00 eixt I1 - 2 dx + a2 ( 2A.4 ) We note that the integrand has poles ...
Página 264
... contour C which extends ( 1 ) along the real axis from -R to a P , ( 2 ) a semicircle with center at a and radius p ... contour integral S eizt -R X α R dx a - p pixt CZ dz α = dx + S giat + it ( pei® ) i do + S eixt a + p X α + · S eit ...
... contour C which extends ( 1 ) along the real axis from -R to a P , ( 2 ) a semicircle with center at a and radius p ... contour integral S eizt -R X α R dx a - p pixt CZ dz α = dx + S giat + it ( pei® ) i do + S eixt a + p X α + · S eit ...
Contenido
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх