# cylindrical coordinates

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## 4 matching pages

##### 1: 1.5 Calculus of Two or More Variables
###### CylindricalCoordinates
1.5.15 $\nabla^{2}f=\frac{{\partial}^{2}f}{{\partial x}^{2}}+\frac{{\partial}^{2}f}{{% \partial y}^{2}}+\frac{{\partial}^{2}f}{{\partial z}^{2}}=\frac{{\partial}^{2}% f}{{\partial r}^{2}}+\frac{1}{r}\frac{\partial f}{\partial r}+\frac{1}{r^{2}}% \frac{{\partial}^{2}f}{{\partial\phi}^{2}}+\frac{{\partial}^{2}f}{{\partial z}% ^{2}}.$
##### 2: 10.73 Physical Applications
In cylindrical coordinates $r$, $\phi$, $z$, (§1.5(ii) we have … On separation of variables into cylindrical coordinates, the Bessel functions $J_{n}\left(x\right)$, and modified Bessel functions $I_{n}\left(x\right)$ and $K_{n}\left(x\right)$, all appear. …
##### 3: Bibliography M
• W. Miller (1974) Lie theory and separation of variables. I: Parabolic cylinder coordinates. SIAM J. Math. Anal. 5 (4), pp. 626–643.
• V. P. Modenov and A. V. Filonov (1986) Calculation of zeros of cylindrical functions and their derivatives. Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (2), pp. 63–64, 71 (Russian).
• P. Moon and D. E. Spencer (1971) Field Theory Handbook. Including Coordinate Systems, Differential Equations and Their Solutions. 2nd edition, Springer-Verlag, Berlin.
• ##### 4: Bibliography H
• P. I. Hadži (1972) Certain sums that contain cylindrical functions. Bul. Akad. Štiince RSS Moldoven. 1972 (3), pp. 75–77, 94 (Russian).
• P. I. Hadži (1978) Sums with cylindrical functions that reduce to the probability function and to related functions. Bul. Akad. Shtiintse RSS Moldoven. 1978 (3), pp. 80–84, 95 (Russian).
• M. H. Halley, D. Delande, and K. T. Taylor (1993) The combination of $R$-matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr. J. Phys. B 26 (12), pp. 1775–1790.