Physical constraints on the coefficients of Fourier expansions in cylindrical coordinates
It is demonstrated that (i) the postulate of infinite differentiability in Cartesian coordinates and (ii) the physical assumption of regularity on the axis of a cylindrical coordinate system provide significant simplifying constraints on the coefficients of Fourier expansions in cylindrical coordinates. These constraints are independent of any governing equations. The simplification can provide considerable practical benefit for the analysis (especially numerical) of actual physical problems. Of equal importance, these constraints demonstrate that if A is any arbitrary physical vector, then the only finite Fourier terms of A_r and A_θ are those with m=1 symmetry. In the Appendix, it is further shown that postulate (i) may be inferred from a more primitive assumption, namely, the arbitrariness of the location of the cylindrical axis of the coordinate system.
© 1990 American Institute of Physics. Received 12 March 1990; accepted for publication 20 June 1990. The authors are indebted to J. L. Schwarzmeier, R. A. Nebel, and M. A. Schalit for many stimulating conversations. This work was supported by the U.S. Department of Energy.
Published - LEWjmp90.pdf