Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 139
... positive 2 Σ J ( r ) sin no n odd positive ( 10.41 ) ( 10.42 ) ( 10.43 ) ( 10.44 ) ( 10.45 ) The left - hand members of Eqs . ( 10.40 ) and ( 10.43 ) are called generating functions of the Bessel functions of integral order . If one ...
... positive 2 Σ J ( r ) sin no n odd positive ( 10.41 ) ( 10.42 ) ( 10.43 ) ( 10.44 ) ( 10.45 ) The left - hand members of Eqs . ( 10.40 ) and ( 10.43 ) are called generating functions of the Bessel functions of integral order . If one ...
Página 282
... positive , say p = aed , a real and positive , then the pattern of Fig . 2C.1 is still maintained but is shifted by 8 in the direction of the real axis , in which the plus and minus signs are for the upper and lower half planes . In the ...
... positive , say p = aed , a real and positive , then the pattern of Fig . 2C.1 is still maintained but is shifted by 8 in the direction of the real axis , in which the plus and minus signs are for the upper and lower half planes . In the ...
Página 291
... positive values of p and v , the error due to breaking off either series after the term m > 1⁄44 ( 2v — 1 ) is smaller than the absolute value of the first term not taken . The asymptotic expansions for J , and N , are obtained by ...
... positive values of p and v , the error due to breaking off either series after the term m > 1⁄44 ( 2v — 1 ) is smaller than the absolute value of the first term not taken . The asymptotic expansions for J , and N , are obtained by ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх