Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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... Integral Representation of J , ( p ) 280 • 2C.3 The Integral Representations of the General Cylindrical Functions . 281 2C.4 The Integral Representation of the Bessel Function J , 283 2C.5 The Hankel Functions 2C.6 Series Expansions at ...
... Integral Representation of J , ( p ) 280 • 2C.3 The Integral Representations of the General Cylindrical Functions . 281 2C.4 The Integral Representation of the Bessel Function J , 283 2C.5 The Hankel Functions 2C.6 Series Expansions at ...
Página 264
Gerald Goertzel, Nunzio Tralli. - If this integral has a limit as → 0 , we call the limit the principal value of I , and denote it by PI ,. To find the principal value of I , we form the integral of elzt / ( za ) along a contour C which ...
Gerald Goertzel, Nunzio Tralli. - If this integral has a limit as → 0 , we call the limit the principal value of I , and denote it by PI ,. To find the principal value of I , we form the integral of elzt / ( za ) along a contour C which ...
Página 281
... integral representations of the Bessel function of integral order . We may use the integral representations to prove that J- ( p ) = ( -1 ) " J ( p ) as follows : In ( 2C.2 ) substitute -n for m . Then J – n ( p ) == R 1 2π -x ei ( p ...
... integral representations of the Bessel function of integral order . We may use the integral representations to prove that J- ( p ) = ( -1 ) " J ( p ) as follows : In ( 2C.2 ) substitute -n for m . Then J – n ( p ) == R 1 2π -x ei ( p ...
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