Topic
Cylindrical harmonics
About: Cylindrical harmonics is a research topic. Over the lifetime, 1068 publications have been published within this topic receiving 24995 citations. The topic is also known as: cylinder functions.
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Book•
01 Jan 1944
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Abstract: 1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices.
9,584 citations
Book•
01 Jan 1955
TL;DR: The transformation of Laplace's equation in polar coordinates and the Legendres associated functions can be found in this article, where the authors also give approximate values of the generalized Legendres functions.
Abstract: Preface 1. The transformation of Laplaces's equation 2. The solution of Laplace's equation in polar coordinates 3. The Legendres associated functions 4. Spherical harmonics 5. Spherical harmonics of general type 6. Approximate values of the generalized Legendres functions 7. Representation of functions by series 8. The addition theorems for general Legendres functions 9. The zeros of Legendres functions and associated functions 10. Harmonics for spaces bounded by surfaces of revolution 11. Ellipsoidal harmonics List of authors quoted General index.
1,678 citations
TL;DR: In this article, the non-diffractive vector Bessel beams of an arbitrary order are examined as both the solution to the vector Helmholtz wave equation and the superposition of vector components of the angular spectrum.
Abstract: The non-diffractive vector Bessel beams of an arbitrary order are examined as both the solution to the vector Helmholtz wave equation and the superposition of vector components of the angular spectrum. The transverse and longitudinal intensity components of the vector Bessel beams are analysed for the radial, azimuthal, circular and linear polarizations. The radially and azimuthally polarized beams are assumed to be formed by the axicon polarizers used with the initially unpolarized or linearly polarized light. Conditions in which the linearly polarized Bessel beams can be approximated by the scalar solutions to the wave equation are also discussed.
244 citations