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1: 1.5 Calculus of Two or More Variables
Cylindrical Coordinates
1.5.15 2 f = 2 f x 2 + 2 f y 2 + 2 f z 2 = 2 f r 2 + 1 r f r + 1 r 2 2 f ϕ 2 + 2 f z 2 .
2: 10.73 Physical Applications
In cylindrical coordinates r , ϕ , z , (§1.5(ii) we have … On separation of variables into cylindrical coordinates, the Bessel functions J n ( x ) , and modified Bessel functions I n ( x ) and K n ( x ) , 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.